Welcome to the final exam review for Math 1220 Calculus II for students at Southern Utah University. If you're watching this video, then this is probably the last video for you of the whole semester. You probably don't need me to remind you, but in case you forgot, this is Professor Andrew Missildine like usual. This is probably not your first rodeo either. We've had several other exams that we've talked about this semester, and so as you probably can expect in this video, we're going to talk about the structure and the topics that are covered on the final exam for Math 1220. There's many things in this video that we're not going to talk about. We're not going to talk about the place, the time, other semester specific details of this exam. Please consult the final exam syllabus or other information you can find on Canvas to learn more about those, because even section to section, there might be different times that you're taking the exam. I can't put that in the video. Look to the syllabus. Look to Canvas for information about that. What we can talk about, of course, in this video is the specific types of things that we're going to see on this exam. In particular, I want to give you heads up on things you should be studying and things you might not have to. What should we know about this exam? This is, in fact, a final exam for Math 1220. As such, this is a comprehensive final exam. This exam covers essentially all of the topics that we have covered in this semester on Calculus II. There are some notable exceptions that I will make mention. Unless I specifically say that a topic's omitted, you should be prepared to study for it. This exam is going to be 15 questions long, just so you're aware. There are five questions in the multiple choice section, usual format as usual, as in the past midterms that we've taken. There should be, I think, five questions in the short response section. Then you count them five questions in the free response section. Again, these are the same structure as in previous exams, so you probably don't need some explanations going about that. Let's focus on the topics that are going to be on this exam. As a comprehensive final exam, it covers everything. This exam is going to cover lessons one through 48, everything we've done this semester.  These will be the first omissions that I should make mention that 49 and 40, 49 and 50, while they are excellent topics, they are optional topics that are not required from for the course description. As such, they won't be manifest on the final exam. We do want to cover topics through from lesson one all the way to lesson 48. As we've summarized this semester, there are a few general topics that we can mention that are going to be represented on this final exam. So first and foremost, calculus two is a class about integrals. We calculate so many integrals throughout this semester. And so when it comes to integration, you must be prepared to set up and evaluate numerous integrals. There's going to be a lot of integrals on this test. So things to be aware of when it comes to integration, we should be able to use various techniques of integration. So things like U substitution trigonometric substitution, rationalizing substitutions, we should be able to use integration by parts integration by cycles integration by hope, we should be able to use algebraic and trigonometric identities, such as partial fraction decomposition. So algebraic trigonometric identities and techniques to help us transform integrals, it transform functions into integrants that are more favorable for integration. These are things we've done throughout the whole semester. A lot on this exam will be focused on techniques of integration, you have to be able to find anti derivatives, no doubt about it. Now, on this exam, sometimes you'll be asked to evaluate an indefinite integral, that means you're going to have to find an anti derivative, don't forget your plus C. There will be some situations where you might have to evaluate an indefinite integral, excuse me. So indefinite integrals were the anti derivatives plus the C. The definite integrals is when you have to then plug in the numbers. Once you found an anti derivative, typically, if you're using the fundamental theorem calculus, I should say, we should be able to set up and evaluate both indefinite and definite integrals. This also includes improper integrals. So we might allow our bounds to approach infinity or negative infinity. We might be approaching vertical asymptotes, we should be prepared to compute in proper integrals, as well as proper integrals. So techniques of integration, calculation of integrals, this will be paramount for this exam. I should also mention that applications of integration will also be covered on this final exam. Now, we have done a lot, a lot of applications of integration, ranging from a variety of topics here. While I'm interested in calculus students understanding the method of integration, this process of accumulation, that is, can we subdivide the problem to small linear problems, and then take limits forming integrals of these Riemann sums. This is things we've done with volume problems, area problems, arc length problems, work problems, hydrostatic force, just to name some of them. Now, as we're preparing for this exam, I do need you to still be able to set up and evaluate integrals for many of these applications. But first and foremost, this is a mathematics class, we've done a lot of scientific and engineering applications. But for the purpose of the final exam, I am not going to ask you any of these scientific or engineering applications of integrals. So nothing to do with work, nothing to do with hydrostatic force, those are the two main ones we're going to throw out. But applications of integrals that have direct consequence to geometric topics, that is fair game. So area, arc length, centroids, surface area, volume, so like the washer method, the shell method, all of those geometric applications, yep, I could possibly ask you one of those types of questions on this exam. So be prepared to find area under a curve or area between two curves, find the arc length or surface area, find volumes of solid of revolution, or finding centroids like X bar or Y bar. Those are all applications that are fair game for this for this for this exam. I should also throw out two other ones to mention the average value and probability examples that we did before. Probability could fall under the umbrella of statistics, but we definitely can put it under the umbrella of mathematics. So we should be looking at applications which are geometric, and you should look at applications which are statistical. So things like the average value of a function, the centroid of a region, the probability that such an event would happen the expected value of a random variable. These are all topics we've done. They are applications of integrals that all have a mathematical flavor to them. And I think this is a compromise that we all can live with. Because honestly, if all the applications we did work in hydrostatic force were probably some of the hardest ones, mostly because they transcend the mathematics, there's you need a good understanding of science there as well. So we are going to have to do some applications of integrals that we will see, like so, I should also say that with respect to integrals, we have some new worlds that we had we explored this semester as well. These are going to be manifests on the exam. For example, we played around with parametric functions, parametric equations. How do you find derivatives and integrals involving parametric equations, a function given by a parameter? This is a slightly different way of approaching functions. And there's the calculus is modified. So in particular, how do you do integrals and derivatives for these parametric functions? Send can also be said about polar functions. Polar functions are equals f of theta. How do you find the tangent line of a polar function? How do you find the arc length of a polar function like the circumference of a limouson? Is an example we could consider? How do you find the area under a polar curve or the area between two polar curves? So this is a slightly new world that we explored. And particularly we focused on the calculus of this new world. And in particular, the focus was on integrals in that situation. And then the last thing I'm going to put under this umbrella of new worlds, I'd also throw in differential equations. Because differential equations, as we said, many times was very much like finding implicit anti derivatives. So like in calculus one, you have differentiation and the explicit differentiation and implicit differentiation, solving a differential equations very much like solve solving an implicit anti derivative. And so it's a new world to calculus. And so we'll put that under the new world umbrella there. So that's the main topics, integrals, techniques of integration, applications of integration, and our exploration into new realms of integration. That's them. Those are the main things that are covered on this exam. But if you were hoping something was omitted, there's other big umbrella to put sequences and series is another extremely important topic that we've explored in this semester. Honestly, series we can put still under this the integral label if you want to. And so while I put in a bullet point, yes, I'm now continuing the list that we started here before, series are just discrete integrals. It's a different type of integral than the continuous integrals we spent most of the semester exploring. But a series is just a discrete improper integral. And we do have to be able to know how to evaluate them or approximate them. Or oftentimes you're just interested in convergence or divergence. And so we are very much interested in convergence test. Can we determine whether a series is convergent or divergent? And why can we justify it? Also, we are interested on power series. This is a very important example to mention, because power series have not appeared on any of the previous midterm exams that we've taken in this course, but they will be manifest on the final exam. So the topics of power series showed up in lessons 43 through 48. 49 and 50 does also involve power series. But like I said, that doesn't actually manifest itself on this final exam. So as you're studying for this final exam, there is this practice exam you see on the screen right now. If you haven't already done so, go find the exit final exam syllabus, go find the practice final exam on canvas pauses video right now to do so if you don't already have them because you want those to help you study. But in addition to the final exam materials, the materials you've used for all of the previous exams are also helpful practice exams, pre exams, the actual exam that you took, you probably have access to all of the solutions to these practice and actual graded exams. And hopefully you've been handed back your graded exams for the previous ones in this course. A lot of the questions you're going to see on this final exam are drafted from the question pools for the other exams you've already taken. So anything you can study from the previous exams will be beneficial for this final exam. But like I said, there are a few topics that will be dropped that won't be seen on the final exam. I am trying to make this into a two hour exam. So we're capping it at 15 questions. But even though there's 15 questions, there is a large variety of topics that we can see on this exam. So we have to be prepared for everything, even though you aren't going to see everything on the test. I also want to point out that when you take the final exam, there will be different versions of the final exam in play. So if you're taking the test and someone next to you is also taking the final exam, you might not have the same exam. Don't plan on it. And so, you know, if luck is a thing, you know, rub your rabbit foot before you get handed out your exam to make sure you get a good version, I guess, because all of the topics we're going to talk about right now could be on the exam, you're not going to see all of them, but you could see all of them. And even if you don't see one of these topics, your neighbor probably will. And saying could go for topics your neighbor doesn't see you probably are seeing. So be aware, this is a truly comprehensive exam. We need to be prepared for all of these different things. I should also mention numerical some numerical integration techniques. This will be very limited. But how do we approximate integrals or series? There will be a little bit on the exam very, very little, but there will be some things. And so I will point your attention to where you should focus on that when we get to it. So with that said, let's now jump into the question by questions, what you might see on the final exam and get really specific on what you should be preparing for. So we're going to start with the multiple choice section. Like I said, there's five questions in the multiple choice. Each of these questions, we five points each. Alright, so question one, you can consider this an integral question. As in question number one is going to ask you to evaluate a definite integral. It could be a proper integral like this one is, it could be an improper integral like we have seen also. So like maybe like this thing goes off towards infinity or something. It could be an application of some kind like it might ask you to find the area under a curve. It might ask you to find the area between two curves. That's what question one is going to ask you to do. It's going to ask you to evaluate a integral proper and proper. So probably the fundamental theorem calculus will be a useful tool here. Other techniques of integration might be helpful. Now question one, the integration shouldn't get too complicated. Now maybe like a basic use substitution, maybe like a very basic integration by part. Those are possible. Like with this one right here, it looks like an algebraic manipulation is probably your best bet to find the antiderivative. But you know, you could do a use substitution. There are options.  So it doesn't matter how you get it. So long as you do it correctly. Alright, so question number one will be an integral question that asks you to evaluate an integral of the different types of continuous integrals we have seen this semester. So question number two, this is one that's very important to focus on because unlike question one, question one, this version appeared on exam one, I believe. And the other possibilities will be grabbed from definite integrals we did like on exam one and exam two, right? It'll be one of something like that. So you can go to exam one and two to study different versions of this problem you've already seen. Question number two, we're going to put a nice star next to it. Question number two is a novel question with regard to the final exam because it's about Maclaurin series. None of the previous exams have covered Maclaurin series, infinite series where they are but power series were not. So can we find a Maclaurin series for the function in this case? It's x times e to the x. What I'm looking for in question number two is that we use the table of important Maclaurin series. Things that like the Maclaurin series for e to the x, sine of x, cosine of x, one over one minus x, that table. You should know that table or be able to produce it on the fly. You should know these standard Maclaurin series. Like for this one, you need to know the Maclaurin series for e to the x. That's most of the heavy lifting. There is this x that's also here which will modify the Maclaurin series for which then you take the Maclaurin series for e to the x and modify it by some techniques and then you're going to find the Maclaurin series for this function here. You of course can use Taylor's formula and produce it from scratch. That's not the intent of this question. There will be a question, the free response that expects you to do something like that. This one wants you to use the standard Maclaurin series like e to the x, cosine, sine and all of its friends that were on that list. Like a binomial series might be an example that would show up here. You should use a standard formula and then slightly modify it to find the correct answer to number two. But number two will ask you about a Maclaurin series of some kind. So let me label this is going to be a power series type question. Alright question number three. Question number three is going to focus on applications. Remember these were the umbrellas that I had mentioned earlier applications of integration. So the version you see on the screen right now this is very similar to something we saw on exam two. This is going to be a numerical integration problem for which you're given the function in a tabular format and using either the trapezoid rule, the midpoint rule, or Simpsons rule you have to approximate the area under the curve. So this is a numerical problem that you could see on the exam where you're approximating the area of the curve using the trapezoid midpoint or Simpsons rule. What I can tell you is what I what you can rest assure is that these are the only numerical topics that you are going to see on this exam. Okay so we've done approximations of series you're not going to see anything like that. We've done some other some other type of numerical stuff. No no no no error bounds. Well am I going to ask you on the final exam if you get a numerical approximation which this is just a possibility for number three it would be trapezoid rule, midpoint rule, Simpsons rule. I mean I guess it could be left or right that's not really focused on in Calc 2. It's probably trapezoidal rule, midpoint rule, or Simpsons rule so you should know how to do those calculations. That's if this is a numerical application. Some other things you should be prepared for so in addition to this numerical approximation you should also be prepared to do an average value. Average value of a function we talked about those on exam one. You should also be able to do some applications with respect to probability. So what's the expected value of this continuous random variable? What's the probability of an event? We talked about probability on exam three. So feel free to go back to those exams. The numerical and the numerical approximations is exam two. This is exam one and this is exam three. So these these will be a multiple choice integral application similar to one of those three multiple choice questions you saw on exams one, two, and three. Alright question number four which you can see on the screen here this will be a series question. Not a serious question, a series question for which much like we saw in exam four this will be a multiple choice question that asks us to determine the convergence or divergence of various series by various tests and in some situations if it's convergent it'll ask you to find the sum of the series. This version asks you which of the following six series is absolutely convergent but some other things we could see here is which of these series is divergent by the divergence test. Which of these series is convergent or divergent by the p test? Which of these series is convergent by the alternating series test? Which of these series is a geometric series and convergent and if it's convergent find the sum of the geometric series. Which of these is a telescoping series? Is it convergent or divergent and if it is convergent what does the sum add up to be? So we saw many multiple choice questions like that on exam four. Question number four on the final exam will ask you one of those series multiple choice questions that we saw on exam four. And now to the last question in the multiple choice section this is the first page of the exam. Question number five will ask you a question about polar coordinates polar functions. On exam four we had three multiple choice questions that are about polar functions. One of them which is about recognizing polar graphs, polar coordinates. One of them was about computing derivatives involving polar coordinates. Like maybe finding the slope of a tangent line to a polar curve. Another question was about finding integrals of polar functions like finding the area of a polar region or finding the area between two polar curves. Finding the arc length of a polar curve. Something like that the circumference of a limouson was an example of those things. So polar functions were covered on exam four. Question number five will ask you a question about polar functions and as every question we saw on exam four that was about polar functions was formatted as a multiple choice question. One of those questions will be grabbed for the final exam. And that then gets us through the multiple choice section. Let's move on to the free response section. Remember free response there are worth more points than the multiple choice but you can also get some partial credit. All that you need for full credit is to have the correct answer on the line but there is space provided to show your work if work is appropriate and you can get some partial credit with that one. Question number six this is also a star problem it's a novel problem because this is a problem that's going to be involving power series. Something that did not appear on previous exams so put special attention to this problem here. Question number six is going to ask you to find a power series representation of a rational function or a function that is related to a rational function perhaps because it's derivative is a rational function like take for example arc tangent of x. It's derivative is a rational function and so utilizing utilizing geometric series we can come up with power series representations for various functions. So this one is going to ask you to come up with a power series representation of the following function in this case you get 3 over 2 plus x minus x squared but remember those sections we talked about 43 43 through 48 this is where we go into depth about power function power series excuse me particularly less than 44 was the main was the main culprit for these type of problems power series representations. So focus on less than 44 as you're trying to prepare for this one. The previous question number two was about the chlorine series and we spent actually three lessons talking about the chlorine series didn't we so you had 47 46 and 45 44 a 40 40 which was a 46 no 47 was the one that has the the chlorine series table you should know that table so you'll definitely want to go to lessons 44 and 47 those are big ones in this final fifth unit about power series all right so then getting to question number seven question number seven is going to ask you to calculate an anti-derivative now question one similar to that so like uh so this is going to be an integral problem again so there was an integral problem in the multiple choice there's going to be an integral problem in the short response there's going to be an integral problem in the free response they're all over the place now while the the problem we saw in question number one the multiple choice who wants you to evaluate a definite integral question number seven will instead focus on improper integrals so we are only looking for the we're only looking for the anti-derivative so don't forget the plus c you do need that for full credit on these indefinite integrals and then these ones the techniques might be a little bit more involved like with this example right here you see there's some trigonometric function in play here cosine of the fourth cosine of the fourth of 2x so trigonometric identities would be very relevant how you should know those trigonometric identities and be prepared to be able to evaluate these integrals using those integration by parts might be relevant so yeah and focus of course on trig identities for this one but any of any of the types of problems we've seen could manifest here because there are going to be some questions in the in the free response to have more involved integrals so while the technique of anti anti differentiation here will be a little bit more advanced than what you saw on question number one it won't it's not as hard as what you're going to see in the free response so this is like the moderately difficult integral question number one was the easy integral question number seven is going to be the moderate integral and then we'll see the free response there's going to be one that's a little bit more challenging so in particular focus on trig stuff here that's probably what you're going to see some type of trigonometric integral you probably don't need more advanced techniques like trig substitution or partial fractions you'll use those later okay focus probably for trig integrals for number number seven be aware of those identities you need to know them all right so then coming to question number eight question number eight is going to be an application type question we saw one of these in the multiple choice we're going to see it in the short response as well what are the type to integrate integration applications we've seen I will list them on the screen explicitly right now so arc length is a problem you should be prepared for and if I read through this correctly yeah this problem in its current form is set up as an arc length problem we should be able to do area problems that includes area between two curves the boundaries might not be given they might be implicit you might have to find them out centroid problems can you set up a centroid problem to find x bar or y bar can we do surface area can we do volume and when I talk about volume I talk about volume the solid of revolution we're focused on the disk method or the shell method I'm not going to do any of those volume problems where you have like a base and you start stacking polygons on top of them or something like that we've done some of those in the past this question won't ask you to do anything like that if it asks you to do volume it'll be a standard application of the washer method or the shell method you should know both of those methods in preparation for this problem so like I said earlier this will be a geometric integration application this problem like we've seen on previous exams so we saw examples like this on exams one and two this will be one where you set up the integral you do not need to evaluate it it will be a definite integral so as you set up your integral there will be bounds you do need to include the bounds if you don't include them you'll be missing something there should be a function you should appropriately simplify the function and there also needs to be a differential of some kind if you're missing the differential you're losing points if you don't have your bounds you don't you've lost some points if you don't have the integral symbol that's also losing points if you don't appropriately simplify the function you're losing some points there so do make sure you have all those things and this applies to all of these set up and do not evaluate integrals like question number nine question number nine is going to be a question about parametric equations we saw in the multiple choice a question about pair of polar functions that is the only question on the exam that'll be about polar functions likewise question number nine will be the only question on the exam about parametric functions now this one is a set up as an integral problem so this one wants you to find the area of some parametric region you might also have to do arc length of a parametric region you might have to do surface area a surface that's rotated around an axis using parametric curves that's possibilities but you also need to be prepared for derivatives right so integral problems and be aware parametric equations we saw this on exclusively on exam three you had a couple of questions in the shore response section that were integral problems involving parametric functions but there were some questions in the free response where we had to set up derivatives like find the tangent line of a polar curve find the second derivative of a polar curve you had some questions like that they showed up in the free response section be aware that for the final exam those questions could be reformatted into short response questions as opposed to the free response questions they were before so be prepared for that question number nine the one guarantees it'll ask you about parametric functions and it'll ask you to either set up an evaluated integral involving parametric functions or a derivative involving parametric functions if it tells you not to evaluate you don't have to evaluate but if it doesn't then you better so be prepared for that remember parametric equations were exclusively on exam three now we get to the last question on the shore response this is another integral technique question I told you there's a lot of integrals on this exam count two was about integrals question number 10 is going to be out integrals you probably should be using integration by parts on question number 10 like if you look this one I hear x times e to the x the best technique is integration by parts just be prepared to use integration by parts it will be manifest on the exam probably question number 10 all right so now let's move to the free response section of the exam free response section of course these questions have different amounts of points based upon their difficulty but we want to be prepared for each and every one of these question number 11 okay question number 11 it's worth eight points it gives you a power series and it asks you to find the interval of convergence given the power series so this is like what we did in section 43 a lesson 43 you're given a power series you have to find the interval of convergence probably the way you want to solve this problem is start using the ratio test to find the radius of convergence once you have the radius of convergence you get most of the interval of convergence but you have to test the end points individually like let's say hypothetically the radius of convergence turned out to be four on this one it's not just so you're aware it's centered at zero so it's like okay from negative four to four you have those and then we have to determine if I plug in x equals four is it convergent or divergent that's like a street fighter series type problem there same thing so maybe like negative four is not included but positive four is again I'm not claiming that's the right answer but you need to find the interval of convergence you do have to check the end points if you do not check all of the end points you aren't going to get full credit on this one okay you do and you have to also check and give some justification on what happens at those end points there speaking of street fighter questions this gets us to question number 12 which is worth nine points in this case you're given a infinite series no x's in play there you have to determine whether it's absolutely convergent conditionally convergent or divergent and you can use any integral test that we are any series test that we know about so we got the alternating series test we have the comparison test the limit comparison test the integral test the geometric series test the ratio test the root test I see that has the same acronym there and maybe I forgot someone I don't know it's always the case you always forget someone it feels like alternate series test comparison test integral test geometric series I feel like we're pretty good the only other one you can talk about like a telescoping series so we have to be able to determine the convergence of these series this is a street fighter question this is street fighter 2 determine the convergence of any series whatsoever now this question is formatted in the same way that the street fighter questions were formatted for exam for exam exam 4 that's the word I'm looking for but there were some short response questions on exam 4 that could be modified into this question as well those are excellent ones to look at as well as you prepare for question number 12 so this will be a question about series infinite series there all right so then we go to the next page of the free response section we get to question number 13 which is worth 10 points this will be an integral question in particular we want to think of this as our as our street fighter integral problem you could be given any integral under the sun and you can use any of the techniques we've learned about so I've said them before but I'll say them again integration by parts use substitution trigonometric substitution partial fraction decomposition rationalize the substitution just to name a few we've had a lot of techniques we've learned question number 13 will be your chance to shine in which case you can evaluate or you'll be asked to evaluate some indefinite integral don't forget the plus C on the previous question about the street fighter series you need to also make sure you include the convergence test that you're using if you believe it's convergent by the alternate series test you need to be explicit and say those things there with number 13 show all the work find the antiderivative here question number 14 is a question about differential equations this will be the only question on the exam involving differential equations in any form whatsoever there's basically two things you should be prepared for with regard to question number 14 can you solve a linear differential equation well like this one right here it asks you to find the integrating factor can you solve a separable differential equation by separation of variables those are two problems we saw on exam 3 question number 14 will ask you to do one thing involving these differential equations and so then we get to the last question which this one gets another star this is a question about power series which have not appeared on previous exams and in particular this will be a question which asks you to to find a Taylor series for a function and so in this case you want to use Taylor's formula so that if you take your series cn x to the x minus a to the n right we want to use Taylor's formula where cn is equal to the nth derivative of f evaluated at the center a divided by n factorial so you're going to have to take the higher derivatives of our function I will give you a function whose higher derivatives become somewhat predictable like the natural log of x there's a pattern that'll be established you could do something like centricosh the hydrophonic functions there's a pattern that'll be established eventually so you can predict what these higher derivatives are going to be without too much difficulty I'll give you a center that's not too pathological and you'll be then asked to come up with the power series the Taylor series for that function you do not have to find the radius of convergence on question number 15 we already did that on question 11 you do not even find the interval of convergence you do not need to prove that the Taylor series is convergent for anything I mean clearly it's conversion on the integral of convergence but you don't need to do that you don't need to use Taylor's inequality to prove that a function is equal to its- It's Taylor series on the interval of convergence you don't need Taylor series ah sorry you don't need Taylor's inequality for this exam because again, you don't need to use any error bounds for this exam whatsoever. So this gets us to question number 15, and there we have it. The basic test feels like the following way. There are three sections, multiple choice, short response, free response. Each of them has five questions each. Each of those questions for the most part have the following feel. You have a question to ask you to do an integration technique. You have a question that asks you to do an application of integrals. You have a question that asks you to explore a new world. On the multiple choice section, we have polar functions. On the short response section, we have parametric functions. And on the free response, we had differential equations. You have a question that asks you to do something with series. So convergence of series, evaluation of series. And then you have a question about power series. Each of the three sections on the exam with their five questions follows this format, clearly not necessarily in this order. The only exception of course in the free response and the free response, there was no application problem. Instead, we got two power series questions. So power series is the tail end of our course, but you can see that there is a high distribution of power series questions on this final exam. You need to prepare for it. And if you feel like, well, that seems unfair, that's just a small part of the semester. Well, it's actually a big chunk of the semester because it hasn't been tested on any previous exams, I do have to cover them so they're gonna show up in the final exam. And the most important thing is that power series as a topic is comprehensive. It is. Everything we learn kind of points towards power series. Believe it or not, power series is essentially the main objective of Calculus II. It's the cumulative topic that covers everything. If we have a good understanding of power series, then we have a good understanding of Calculus II, which is why it's not unfair to ask many questions about power series on this exam. All right, so with that said, we're now at the end of our exam review and essentially at the end of the semester, right? Whether you're gonna take the final exam in a couple of days or in a couple of seconds, hopefully you're prepared, hopefully you do really well and hopefully I don't see you next semester in Calculus II. I definitely want you to pass this exam. It's an important exam and it does have a big impact on your final grade so we all want you to do well on this. Of course, if you have any questions whatsoever, reach out to the resources that you need. Reach out to me, I'll be glad to help you out either during office hours or even outside of office hours. I wanna help you as much as I can. Utilize the tutoring center, work with classmates. You can do this. You're gonna have to put in the effort. This final exam is a big exam. I mean, if I'm being honest, it's probably gonna take 10 hours of study to get a good grade on this exam. I'm trying to be honest and frank. It takes a long time to get a good score on an exam and this is 10 hours assuming you've been, of course, active in lessons and other assignments as well. If you are grossly behind, you're missing some work, it might take a lot more effort to make up what you didn't get from those assignments. So I'm assuming if you're watching this video, you've made it to the end because we're about 40 minutes right now, you probably are a dutiful student who is eager to work hard and take this exam and do fantastic. Keep on doing it. If you've done well this semester, I expect you'll do well on this final exam as well. Best of luck. Let me know if you have any questions and let the, and may the force be with you.


Hello and welcome to NewsClick. I am Aditi and this is the Daily Roundup. I am Prashant and here are the major stories for the day. Our top story for the day comes courtesy of PepsiCo, who are sowing nine farmers in Gujarat seeking damages of over one crore each for allegedly growing and selling its laze variety of potato under the Protection of Plant Varieties and Farmers Rights Act. These are considered among the first cases of alleged intellectual property rights infringement against farmers in India. NewsClick reporter Sumedha Pal was at the press conference in New Delhi where the All India Kisan Sabha addressed the issues from the farmer's standpoint explaining why this is a huge bogus case. She sent us this report. Let's have a look. Conference which has been organised by the All India Kisan Sabha about the case that PepsiCo has filed against innocent farmers from Gujarat. There were nine farmers who were sued by the corporate giants for using a certain variety of seeds also known as the FL-2027 or FL-205. So this is a variety of seeds that PepsiCo had accused the farmers of using and violating the patent of PepsiCo under the intellectual property. And they had said that the farmers had stolen the intellectual property rights of PepsiCo and this is why they should actually pay a compensation of rupees one crore and even more. Today the case hearing had taken place earlier and where PepsiCo has opted out to do an out of court settlement with the farmers and asking them to actually file written responses as to how this intellectual property violation was allowed to take place. They have also asked the farmers to destroy the kind of seeds, the variety of seeds that they had which is patented by PepsiCo. Now we are at the press conference today where we've spoken to Hanan Mola as well of the AIKS who has told us about what kind of steps are being taken to launch a campaign against PepsiCo and the kind of response that is being seeked from the big company. The activists on the ground are calling for the corporate giant to actually withdraw the case and the out of court settlement is actually nothing but a token attempt. Take a look at what he had to say. They appointed a detective agency private, they went to the field without informing the farmers, without informing the government and clandestinely they collected information around the basis of that they went to the court and they demanded this compensation. But our question is in the same act, it is mentioned. Not to be understanding whatever mention in this act, farmers have the right to use, so produce, reproduce all these seeds, they have the right. Article 391 is there, but there is certain provision, some restriction there. The branded seeds they would not be able to use. But other things they can produce, that rights are there. But we found that this foreign company, multinational company they are exploiting this far poor farmer to three acres land there from where they will get one and two point two kilo. And they cannot fight even in the court also. So we demanded this court, the PepsiCo should withdraw the case immediately and government should take action for the immoral, illegal way of collecting information against the farmers. Moving to Madhya Pradesh, there have been reports of a number of fake farm loans that were extended under the previous BJP government in the state. Farmers claim that the loans were taken in their names without their consent or knowledge. In some cases, these loans were extended even to dead people. Only after the current Congress government implemented the Jai Kisan Rain Mafia Yojna and lists of farmers who had received waivers was handed to panchayats did the farmers realize from different villages, Gwalior, Sagar, Indore, what was going on. Kashif Kakui reports. The farmers who did not receive waivers still got a salary of Rs. 1.5-2 lakhs or Rs. 1 lakhs in their names. Many farmers, the secretaries of the society have been deported to their homes by the secretaries of the society. The money that goes is not given to the farmers, it goes to the secretaries of the society. In Gwalior, the roughly idea that comes to mind is that the money is going to be Rs. 245 crores. And I still believe that the money is going to be Rs. 70 crores. Many people who are landowners, many of whom are called landowners, they are not from the Rajaswale family, they are not from the land family, they have been deported. The people who do not live in the village have been deported. The people who have been deported for the past 10-12 years the people who have been deported for the past 10-12 years have been deported for the past 10-12 years. And many of them have been deported for the past 10-12 years. The farmers do not know that they have been deported. They have been deported for the past 10-12 years. If this entire tax system is out of trust and if the tax system is mixed with the shopping centres, then this is the biggest issue in the country. We will leave everyone behind. From MP, we moved to Begu Sarai in Bihar where Basha Singh caught up with CPI Lok Sabha candidate and ex-JNU Students Union President Kanhaiya Kumar. The constituency goes to polls in three days on April 29. This fight is a fight for justice. On one hand, I told you how the forces are who are basically looting this country. And they are not justifying their loot but they are serving the country. Looting the country cannot be served. The country is going through many kinds of problems. On the other hand, there are ordinary people who are calling their voices against it. So, the support and support of all the people is moral and economic. We have made a contribution of 100 rupees in crowdfunding. Some are physically coming here to campaign and roaming around the tea shop, talking to people. So, gradually, people are contributing. No, some are asking for blessings from far away. They are giving blessings. So, this fight is...  It is not about a person. No, as a symbol, people are watching Kanhaiya. Kanhaiya is Begu Sarai's son. Kanhaiya is the face of the campaign for the democracy and the constitution. How is this an individual for you? I think that all things are not fixed in life. You will not be fixed that you will have a problem. You will go through those paths where you will not have any imagination that there will be a district of any country where you have not reached at all. Whereas, this quote-and-quote is considered to be a developed district of Bihar. You are seeing the situation of it. You are roaming with us. So, life creates circumstances and as a human being, you have to face it. We never thought that we would fight a elections. We never thought that all these people would feel their own way or that they will somehow get connected to our elections. So, that happened. I believe this is a positive sign and I do not have any pressure because I do not have anything to lose. Look, in India, the politics of caste and religion continue to be political. This is a very old thing. The new thing that needs to happen and that should happen is that issues-based politics will emerge. Right-based politics will emerge. And when we say that a good school should be formed, then all caste and community people will be associated with it. If the school is good, then all the caste people will study it. All the religious people will study it. If there is a good hospital, then all the treatment will be done. If there is a good road, then everything will feel good. If there is a good breeze, it is not that the breeze is bad, then it is said that no, we will destroy the lor cast, and we will not cast it. These are the questions that are emerging in the world. The problem is that whatever established political party is on either this side or that side, those who fight with caste and religion and with social engineering, will fight with it. In Begu Sarai, all those political parties will be destroyed. I believe that. To watch the entire ground report from Begu Sarai, keep a look out for the latest episode of Pulse of India with Basha Singh. For an international segment, we are joined by Prashant Radhakrishnan. Our first tourist from Colombia were hundreds and thousands of people took over the streets as part of the historic national strike on April 25th. These protesters came from all walks of life. There were students, teachers, doctors, pensioners, but they had one demand in common. They wanted the right to life, liberty and justice, and rejected the policies of the Ivandu government. The government responded by mobilizing nearly 20,000 soldiers in addition to paramilitary forces. In the capital of Bogota, the notorious paramilitary force fired tear gas on the protesters and even manhandled some of them. However, this did not break their spirit and they kept gathering in large numbers. The principal demand of the people who participated in the strike was that the government implement the peace agreement signed by the previous government with the former guerrilla group FARC. The other key component was regarding the national development plan which is being discussed in parliament right now. Many organizations have pointed out that this national development plan is based on an extractivist model which loots the resources in the country and provides great benefits to corporates while the people and their livelihoods suffer. Various sectors of Colombian society brought their own demands to the strike. For instance, teachers and students pointed out their education was heavily underfunded. Doctors, on the other hand, pointed out the various problems afflicting the health sector in the country. One key demand raised by many organizations was the fact that ever since the peace agreement was signed in 2016, there has been a marked rise in the assassination of social leaders. Nearly 600 social leaders have been killed since 2016. In our second story, we take you to Iceland where the credit card processing company, Valitor, was asked to pay 10 million dollars to WikiLeaks for not following the 2013 Supreme Court judgment on the issue. Valitor had refused to process payments to WikiLeaks and as a result was fined. In 2010, all the major credit card processing companies in the world including Visa, Mastercard and PayPal decided to ban any payments to WikiLeaks after WikiLeaks published documents exposing the secrets of governments of the world. In 2012, WikiLeaks appealed in a court against Valitor claiming that the ban was extrajudicial. The Supreme Court in 2013 agreed and asked Valitor to resume payments however they did not do so and this judgment was pronounced. Earlier this month, WikiLeaks found that Julian Assange was arrested in London after the Ecuadorian Embassy withdrew its asylum. He now faces an extradition hearing on May 2nd based on a grand jury indictment from the United States. Assange is charged with trying to crack a US defense department computer under the Computer Fraud and Abuse Act. Of course, these acts refer to basically the publication of documents from US war crimes and were given to Assange and WikiLeaks by Chelsea Mani. That's all we have time for today. To find out more about these stories check our website newsclick.in and subscribe to our YouTube channel. Thank you for watching.


The speed of light, a cloud of dust, and the hockey-high old silver, the lone ranger! In companion Toto, the daring and resourceful mask-rider of the plains led the fight for law and order in the early western United States. Nowhere in the pages of history can one find a greater champion of justice. Return with us now to those thrilling days of yesteryear. From out of the past come the thundering hoofbeaks of the great horse Silver. The lone ranger rides again! Monk Silver! Let's go big fellow! I am Silver! Then the fastest yet, he can loop the loop because he knows... Every breakfast and you'll get go-power too. Because a Cheerios breakfast is loaded with proteins, vitamins, and minerals. The very things that help build healthy bodies, strong bones, good red blood, and muscles. Why they'd be the sort of breakfast you'd go for even if they didn't taste so good. And they do taste delicious.  So that's for you, swell-tasting Cheerios and milk for go-power. Eat them every morning and you'll hear... He's feeling his cheer! Brother notorious Martin brothers Casey and Dad. Rob the Allen City Bank and escaped after shooting three persons. They fled in an easterly direction, but in order to throw off their pursuers, backtracked and continued to the west. Seldom resting, eating hardly at all, the outlaws continued to ride for three days. Then when they and their animals were at a point of utter exhaustion, they halted. Oh, oh! Casey Martin called his brother to one side and said... Ab, if there was anyone following us, we'd be shaking them off by this time. Yeah. Casey, we're in sad shape. The horses are almost finished. The boys are hungry. I know, I know. So whether we like it or not, Ab, we have to take a chance on being seen while we try to get food and horses. Have any idea where we are? No, we've never worked this part of the country. The kid says he's been here before. The boy says there's a town called Dunmore, west of here. Few of us are going there with him while the rest stay here. We have to rustle up some grub and some new horses. Maybe something to drink. Ab Martin, the kid, and three other outlaws, including one called Johnny, reached the outskirts of Dunmore in the afternoon. Ab made a decision. Kid, there's no chance anyone will recognize you. You go into town now and order the grub and look for the horses. The boys and I'll go in when it's dark. Well, stay at some cafe till about 10 o'clock and then meet you. Well, hide over there among those trees till dark. Here on Papa, in the wild hills to the north of Dunmore, stopped at the gold mine of Prospector Jack McVeigh, a man they've known for many years. I was surprised to see that the entrance to the mine was blocked by a massive round boulder, which Jack was trying to remove with no results. Jack, after greeting them, said... The last time you were here was a year ago, in the summer. Ah, it right after you start to dig here. I did a lot of digging, too. Kept at it all summer and fall. What's to dug 40 feet straight through that hill, right behind the rock? What's the rock doing there lodges in the entrance? Man, do you know how it snows and blows once winter sets in up here? I do, Jack. Well, it's really bad. Bad? It's the worst. Once the snows started, I scooted out of here. But first, I used my mule to help me push that rock again the entrance to the mine. Now I can't move it away. Well, stop worrying about it, Jack. Toto, take this spade and start digging a shallow trench away from the boulder. Ah, me do it. I'll use your pick, Jack, and loosen the dirt that's holding the boulder tight. Toto dug a narrow trench from the rock to the top of a small incline that leveled off about 10 feet from the mine entrance. Then when the boulder was loose, they rolled it along the trench as a train might roll on a track. They stopped when the boulder rested on level ground. Jack McVay thanked them and invited them to eat with them at his cabin a mile away from the mine. But the Lone Ranger declined. Oh, no thanks, Jack. We'll set up camp as we always do. We'll not be too far away. Perhaps we'll see you in the morning. At that moment in Dunmore, Deputy Sheriff Rudy Carmack, breathless and pop-eyed, burst into the office of Sheriff Tom Wayne. Ed Martin. It's him, Sheriff. It's him, all right. I'm sure. What are you talking about? Ed Martin, the outlaw. He and three other fellas are sitting at a table over in Kick Glass Goes Cafe. Look, the report we got from Alan City, said the gang headed east after they robbed the bank there. I don't care what the report said, Sheriff. Ed Martin. All right, all right, Rudy. Round up every man you can get. Do it fast. We're going over to the cafe and take those arm rays. Come in to Dunmore right in the open, would they, huh? Come on, we'll show them. There were 10 deputies with Sheriff Wayne and Rudy Carmack when they rushed into the cafe and covered Ed Martin and his pals. Don't move, Martin. You're under arrest. Look out, Sheriff. Don't shoot, Sheriff. You're waiting to open. Don't shoot again, Sheriff. We'll give up. You're fooled us this time. Throw your gun in, Johnny. That's more like it. Pete, get those two-handed arm rays in the dockies. Ed will take you and your pal to our jailhouse for a while. Go to it. You never hold us there. No. You're right. Because we're putting you and a stagecoach and driving you back to Allen City where they want you. We'll start looking for your brother and the rest of the gang tomorrow. Sheriff, I'm going after that stagecoach. Rudy Carmack hurried to the stable and sought out the owner. Josh, get your stagecoach fixed up, huh? The sheriff wants to hire it. Sure thing, Rudy. Say, that was some excitement you had over at the cafe, huh? Yeah, I called Ed Martin and another outlaw and shot two others. That's what we want the coach for, to take Martin and his pal, Allen City, tonight. We figure if we leave right away, we'll get there. As Rudy Carmack talked to figures standing in the shadows, seemed to melt away from the stable, the young outlaw known as the kid had heard enough. He hurried to where his horse was tied, mounted it, then headed for the hills and the place where he knew that Casey Martin and the rest of the gang waited. Take some to Allen City, isn't what we rode on today? Those filthy, slithering rats taking Ab and Johnny like that. Well, they're not going to keep them. You're going to try to hold up the stage, Casey? We'll blast the stage in every tin badge rabble that's guarding my brother.  We've been waving here for more than an hour now. You sure this the road they'll take to Allen City? I am Casey. I'll check when I was over here. Coming around the bend in the road. It's a stage, Coach. There are four riders with us. Guards. There are none of us. Boys, blast the guards first. The outlaw's initial burst of fire sent three of the guards tumbling from their horses. The fourth rider and the shotgun guard returned the fire. What the outlaw's attack was as relentless as it was unexpected, bullets wounded the fourth guard and one of the lead horses on the coach. As the wounded animal fell, the other horses piled up and each coach careening turned over. We're in shotgun guard. We're thrown to the road unconscious. Oh, it's a fire, boys. No more. Abs inside that coach. Ab and Johnny. We've got to get them out. We've got to get them out. Well, Casey, we've got Ab and Johnny out of the coach. They're banged up bad. Not as bad as a sheriff and that deputy. What are you going to do, Casey? What we plan to do, get away from here as fast as we can. Let's get Ab and Johnny onto a horse. All right. The curtain falls on the first act of our lone ranger adventure. Before the next exciting scenes, please permit us to pause for just a few moments. That Bobby is the boy of nine. He can really hit that line. He's the star because he knows. Nourishing because they're made from oats with minerals, vitamins and proteins that your body needs. Yes, indeed. A bowl of Cheerios and milk really starts your day off right. All sorts of good things for your body helps you have strong bones and muscles, good red blood and healthy nerves. So every morning, take on a bowl of Cheerios and milk for real go power. You like that wonderful toasted oat flavor too. Downright delicious. Come to think of it, Cheerios is one of the tastiest muscle-building foods you can eat. Try Cheerios and you'll hear... He's feeling his Cheerios. To continue, as high in the hills he had trudged on relentlessly for five hours. Casey Martin leading the horse that carried his brother called through the darkness. Kid, I think you got us lost. Doesn't seem to be any direction to where we're going. I'm sorry, Casey. There's only more moonlight. Maybe I could just... Casey. Boys look there behind the trees. It's a light. It's a cabin, boys. You see? That means grub. Let's go there. Get it. Prospector Jack McVeigh and his cabin had lighted the lantern when he heard hoofs and footsteps somewhere nearby. He walked to the door and opened it, as Casey Martin and the kids stopped outside. Ben, who are you? What do you want? Hi there, Pop. Who's with you? Nobody, but I asked you a question first. I know these are boys alone. Leave the horses come on in. Wait a second, you. Out of the way, old man. Why are you young whippersnapper? I'll bash your head for pushing me. Stop waving that lantern around like that. You're getting oil all over the floor. Give me that lantern. It's covering snakes. Hey, fire. The place has done fire. Casey, get out. Get out. We can't stop you. I know. Get away. Hold on in a second. Did I told you to watch out? Where is that old geezer? Damn, you're fire-setting devil. Knocked out. You'll lout your broker's head just for that? The blaze overheated a drum of coal oil inside. Things are spreading. There'll be a forest fire. They got a horse with ab on it, and let's get away from here. Can't stay here. Move back. The lone ranger and Toto in their camp less than a mile away saw the flames, heard the explosion, and rolled through the night to the scene of the fire. Oh, oh, oh. Easy, Toto. Easy, Toto. This is Jock's cabin, Toto. There he is. Over there on the ground. Let me see him. Other man beside him. Let's drag them out of harm's way. Come on. This is far enough. Hit me again and out. Easy, Jock. Easy. You're all right.  Oh, shoot. Lie still, Jock. You'll be all right. Other man's bad shape, Kimusabi. He'll not come too easy. What man? Oh, young coyote, huh? I did that to him.  That's what I did. Jock, the fire's not going to spread, but it's too late to do anything about your cabin. So tell us what happened. Excitably but briefly, Jock related the events leading to the fire. The lone ranger asked, Jock, are you well enough to look after this young fellow? I am. I'll tie him up just to make sure he doesn't try any funny stuff when he comes to. That'll be a long time from now, I think. Come on, Toto. Let's go after the others. We'll tie their horses to a tree, then quietly make their way through the underbrush till they reach the spot near the group of men. They can hear the crooks' words and phrases from time to time. There's no floor. All right, girl. Let's go back and get this kid. Oh, he's the same. Let's get away. We love over there. A lot of man's somebody. We're going to have to find a place to hide to have some bad shape. When one of the men lighted a match, the lone ranger and Toto saw three faces in the pale yellow flare. Toto, that's Casey Martin. Man with an outlaw, too. That's a gang every sheriff in the west is looking for. Toto, you right back to Dunmore. Get the sheriff and all the help possible. Well, I'll try to join the Martin gang. Come back here a bit so we can talk more freely. The fleeing Martin gang, some of them still badly hurt, reached a decision after a meeting of many minutes. The leader, Casey Martin, accepted it. All right, boys. We'll set up guards and rest here an hour or two. This is a bad place to live. Freeze, mister, move in our soup. Why, Casey? I came here to do things for you. He knows you, Casey. Sure I do. Now, you too, Raffo. New Gilligan and Jamesy. Hey, who are you? How do you know us? Anyone who knows anything about real outlaws knows you boys. Funny, I could meet you up here. What's the idea of the mask, stranger? Why do you fellas wear bandanas at times? People I know wear masks when they do a job. I'm just different enough to wear mine always. Never mind the talk. Maybe you're somebody we don't know. This isn't our territory. Don't I know it? Now, look, it'll be dawn soon. This is a bad place to be congregating. It sure is. I have to shoot him up a sheriff in his man.  He's a trap shot. There's a hideout just a short distance from here, Casey. Nobody knows about it but me. I'm heading there now. I heard you fellas. You have one where? Just over the ridge in a cave.  Horses and all. I'd like to take you there, Casey, if you and the boys want to go. If you don't want to, it doesn't matter to me. Casey, do what he says. I'm weak and need a rest. Me too. Well, I don't know what to do. Go on, Casey. All right. Doing this for you, Ab.  But a mask means only one thing to me.  So leave the way to this hideout of yours. Leading silver where Tata was hiding. The lone ranger unerringly led the remains of the Martin gang to Jacques McVeigh's mine. There were letters inside and the men lit these. All right. Casey, give me some water. Sure, Ab. Wait till I get my canteen. Well, you boys are settling down here. I'll get rid of the prints outside.  I'll be seeing you.  Casey, the water, please. Oh, sure, Ab, sure. Here. Take some. You now, Ab. Hey, Ab, do you get a look at that mask out there? Yeah. Something about him I don't like. It's as if it... Wait a minute. I'm sorry, Ab. Hey, boys, I just thought of something. There's one masked man in the West who's not an outlaw.  I'm going out and find out if this would be the armed raid. Casey Martin, his eyes suddenly bright, ran from the mine into the night. Hey, you, masked man. Where are you, masked man? Over here, Casey. Where? Hey, what are you doing to that boulder? You're pushing it. Well, you double-crosser, I know who you are. You're the lone-ranger.  Stop that gun, Casey. No, I'll... Boys! Boys! All right, take it. No! As Casey fell unconscious from the punch, the lone-ranger ran to the boulder. He stood behind it and with a mighty effort pushed. The giant boulder in the groove made earlier rolled down the incline and slammed tight against the opening to the mine. Strike right in the middle. Stop shouting. You're locked in there until the law comes. Go ahead. Push against the rock, all of you. You'll have to squeeze through to get out. And it'll be one at a time. I'll have my guns ready. Waiting. Late that morning, Tonto appeared with Sheriff Wayne, Rudy Carmack and other deputies. Jack McVeigh, who was with the group, spoke first. How do you know, man? You have them cooped up in the mine just like Tongo said you would. Yes. Casey Martin tried to come out. You'll find them bound tightly over by the tree. Brother Abbott's inside with the rest. They ambushed us last night. Almost killed me and my men. Lucky we're tough, we survived. Me, too. Burn the place down they did and bash me. Only I bashed a little myself. That whipper snapper's head will be getting fixed with five doctors for weeks. That lad was an outlaw. A kid, they call him. Well, they'll call him by a number now instead of a name. That is, if they don't hang him. He told us they have the Allen Bank money with them. Well, let's get it. Me and Cuffer that open. All right. A few of you worked that boulder away from the entrance. All right. Now, if they've massed ma'am with only... See, they've massed ma'am. He was here a second ago. Where is he? Well, that Indian was holding a white horse. See, the mass man's on it. They're waning to us and they're riding away. That's the way he always does. Works by himself till crooks are ready for capture. Then lets the law step in. Yes, sir. We heard them say that. And I guess it's why they call him the known ranger. All right, Ben. Let's open that man. Yes, champions are made, not born. That's the American way. Here's how one famous basketball champion got started. Jim Pollard of the Minneapolis Lakers. They called him Little Jumpin' Jim. Nothing short of the top for him. He practiced rebound layups too and followed what the champs all knew. Wheaties for breakfast so good for you. Today Jim plays with lots of bounce. Still eats his Wheaties every ounce. Jim Pollard started eating Wheaties when he was 11. He's been eating them ever since 21 years. Solid food Wheaties. There's a whole kernel of wheat in every Wheaties plate. Let's go Jim down the floor. On his way, on his way. He's on his way, on his way. Get on your way with Wheaties. Cause champions are made, not born. Yes, sir. Get on your way. Get on your way. Get on your way with Wheaties. Breakfast of champions. The copyrighted feature of the Lone Ranger Incorporated is created by George W. Trendle. Produced by Trendle Campbell Muir Incorporated. Directed by Charles D. Livingston. And edited by Fran Stryker. The part of the Lone Ranger is played by Brace Beamer. Your announcer, Fred Foy. Lone Ranger is brought to you by General Mills every Monday, Wednesday and Friday at this same time. Be sure to listen. This way.


Let's get going again. You've seen some of the charts I was pointing to. Let me give you a bit of a summary as to what I was referring to there. Now, basically, we've had a bit of a sell-off last week. We've pushed into what I would call the kind of cliff edge.  That cliff, for me, quite well defined in the S&P 500. And it's 1800. They're sort of 1800 to 18, maybe more specifically, sort of 1,820 kind of area. It's some pretty hefty support. And we did dip down into the lowest in two years. Thereabouts in the S&P 500 last week, but we've rallied pretty strongly back. Now, if we look over to these other charts we were just looking at before, we can see that similar things have happened in Europe. Now, we've dipped below the 200-week moving average in Germany. But we've pulled off before we reached this low from October 2014, we've reacted before we got there. Still a chance we can dip down there. That's my base case scenario that we probably do get down there. But at the moment, seeing a bit of a pullback off the lows, we've kind of held this support here, which I had on the chart. We've obviously dipped through it, but we've closed back above it. Kind of reacted from this open to this lower candlestick here. Now, looking at the footsie as a basis for comparison, you can see we did made fresh three-year lows, but have seen a strong bounce back. And that's continuing through today. Part of what really set us lower last week was this sell-off in financial shares. If you pull up a chart of looking at the financial sector versus the 2100, I don't have a chart for the financial sector right here. But the general idea is that it's been massively underperforming the general benchmark. And part of the reason is that we've been moving towards lower interest rates. And obviously, it recently kicked off really by the Bank of Japan. We've seen a shift into negative interest rates. And Japan's 10-year yield, so the yield on their 10-year debt turn negative. So if you want to borrow for the next 10 years in Japan, you actually have to pay for the privilege. So if you want to buy bonds for parking money in a safe area to earn an investment, you're actually paying for that privilege. Things have got pretty distorted. And that's not a great environment for banks, because they typically try to borrow at the long end and then lend to you at the short end, making the interest rate difference a bit difficult when it's negative at the end they want to borrow from. It just confuses things. So today, we're getting a bit of a bounce back. There's just been a few positive news items out to the banking sector today. The example is that HSBC is staying in London. They had some decent earnings from Commerce Bank at the end of last week. JP Morgan chases Jamie Dimon, buying, sorry, Morgan's. Yeah, JP Morgan's, I was going to say Morgan Stanley, but it's too many Morgan's. The CEO has bought $25 million worth of stocks, showing some faith in the sector. So a few things supporting the bank shares. They're lifting the footsie today.  So if you take the aggregate of it, not so much reason for China to sell off dramatically. And probably the biggest news over the weekend was the interview release from the People's Bank of China governor just saying that essentially that there are no plans to drastically devalue the UN. But you can sort of see that from what they've been doing. They've been massively intervening to sell dollars and buy up the UN to keep its value. They're trying to keep the UN constant against the basket of currencies. And he sort of dismissed the dollar volatility as just a sort of byproduct of that. Obviously there's a lot of big hedge funds out there who are actively shorting the UN in the belief that China's slowdown means that their currency should be worth less. And that's the last part of what's called the turmoil at the start of the year. If the UN can stabilize, perhaps even, excuse me, appreciate a bit over the next week or so, I think that would improve sentiment. And that could be a reason to build a bit of a base of that 1,800 level in the S&P and other global markets. Now I think I mentioned in this recording that Mario Draghi, speaking at 2 p.m. GMT today, have a quick look at the euro. Interestingly, with the euro in the massive sort of fell-off that's taken place, the euro has rallied. Largely, the economic data from Europe hasn't been fantastic. German industrial production saw a surprise drop, multiple other indicators that weren't too impressive. But nonetheless, the euro picked up and declined at the end of the week, matching the jump in equities. And I think it's basically explained by the idea that in these kind of risk-off market environments, European investors are pulling their money back into Europe from overseas. So what's the situation here? Well, if we pull the charts out a bit, now we see that we're in this range. Now obviously, now that we've broken out, the opportunities for going along are slightly diminished, but still, you would think that eventually, the default in this kind of range-bound environment is probably to try and re-challenge 115 again. Or I have this line on there, which I think connects a few of the peaks quite nicely, it's about 114.60. That I think would be the target, but we've seen a bit of a drop-back off the peak last week. Chance in the shorter term for a bit of a drop-back, I think 110 is probably the real line in the sand. That's what we were bumping up against, 110, and we turned into this triangle pattern and we've got the dramatic breakout. So we'll have to see what Mr. Draghi has to say later today. One of the interesting things that happened recently, and it happened, I think it wasn't necessarily, there's, it might have been actually the Wednesday, I can't remember if it was the Wednesday or the Thursday, but basically, Mario Draghi and Karoda, the Bank of Japan governor, both, one of them announced that there's a good chance of easing in March, that was Draghi, the other announced the negative interest rates, but the yen and the euro did precisely the opposite of what they would have intended, are you going up? Not particularly helping their exporters. So we'll have to see what the reaction is to Mario Draghi. If the euro jumps again, he's really lost a lot of influence and that was one of the main catalysts for European stock markets rallying was ECB stimulus and Draghi talking up the prospect of more stimulus. If he's lost that ability, it takes away a lot of the kind of catalyst for why European stocks are rising in the first place, which is evident enough because we're now pushing into multi-year lows. Look at sterling. Sterling has the most of the on the economic data calendar. I mean, it's sterling that kind of dominates this week. That kicks off tomorrow when we've got inflation data out, CPI, obviously meant to remain pretty low levels given the drop-in in all prices, but nonetheless, CPI year over year is expected to tick slightly higher to 0.3% from 0.2% in December. And so we have the FMC minutes which is obviously going to impact all dollar pairs on Wednesday, but we do have, before that, we've got the unemployment rate and the average earnings data on Wednesday, and we round things off for the UK with retail sales on Friday. So what we're looking for here kind of technically is for office economic data is reasons to judge whether this rebound or for lows in the pound is sustainable. So what we've seen is a couple of doji sewing in decision right above the 140 mark, the 140 handle, a big bullish breakout, then we pull back from this peak from April 2015, come back, re-challenge the breakout area and close back even. So at the moment, to me, it is on the bullish side. We haven't broken to the top side, but that is quite significant support that held for a long time, we've broken it, we've retested it, we've come back and challenged, but there's a chance we can push through. But if we can't, then that's, you know, then the default. This really is the line in the sand for me, this sort of 146 30 type area. If we can't push through there, that to me is probably rolling down belief 140, but if we can close a week up to there, then maybe this decline is over. So we've successfully challenged the breakout area, but we've not successfully broken above that previous support 10 resistance. So that's the next, as I said, line in the sand really. Dropping down slightly to the daily chart. Here you can see that kind of resistance building up right beneath the 146 level. And it's been actually consolidating with pretty narrow opens and closes right in at 145. So a bit of indecision about where this is gonna go, but I think by the end of this week, we'll have a much better idea. Not only for what economic data that I just mentioned, but I said quite decent chance, supposedly, that PM David Cameron will have some sort of deal from Europe. And potentially set the date to the referendum. Now, some of the most dramatic moves that we've seen recently have come from the YEN. This is the weekly chart. I mean, this is fairly textbook. We've got declining momentum. We've got a trend line here at first broke. We've got a run down to a fairly well-defined support of 116, a bounce, a retest of the broken trend line, and then just plummeted down right towards the next logical area of support. They're actually rebounded since getting there. So to me, this is pretty much a topping pattern here.  And, you know, there's a chance a few people could get caught offside around 116, but to me, 116 is pretty tough resistance now. It was strong support. It should be strong resistance on the way back up. So if we can get anywhere close to it, that to me would be an area of possible weakness for Dolly Yen. Dolly Yen correlates pretty well to stock market, so we'll have to see, you know, if there's a massive return to some risk-on sentiment. You know, if the Bank of Japan maybe managed to convince us they're able to do more than just the negative rates that they've done so far, perhaps more quantitative easing, then that could all work together to help Dolly Yen and their inequities move on. I think Brent is the most, sorry, WTI is actually the most obvious bottom, but I was looking at Brent today in the chart forum, but here you can see, so good here, basically a fake-out to the bottom and then just a nice rally up to the support, and then we've opened above that today and we're pushing higher. So the next logical stop probably would be this declining trend line here, which kicks in around 31, and then I can probably get into a little bit more detail on Brent since that's what I updated today. You can see that Brent's actually slightly outperformed, basically, rather than the lows that it re-challenged, like WTI is basically just held off of 30. Brent's the international benchmark and $30 per hour is a round number, and few days couldn't get through it, now we're pushing back up. So my default assumption is couldn't push to the downside, tested the bears, they failed. Let's get up to the top and see if the bulls can get us a breakout through 35. If we can, I think that's probably a bit of a game-changer in the intermediate term. 235, given the volatility in all prices, could carry us pretty quickly to 40, 45. Gold, obviously the other big lever. This is a weekly chart here. I mean, I'm showing a lot of weekly charts this week, but I think it's just because of the size of the moves that have been taking place, it requires me to scale out a bit just to give them some context. So a lot of opportunity here. I mean, anyone who's long gold last week, well done. Massive move higher. We did allude to, in the chart forum, this fake out to the downside, the fact, you know, similar thing I was talking about in one of the other charts I've just looked at, where you get, you know, a marginally lower low, but really nothing too convincing. I think it was, yeah, the UK 100. But, you know, if that's all you can do to the downside, then you're opening up a capitulation once we get back above there. Anyone who got short on a breakout's gonna give up.  And that contributed to this massive move higher. So we've got this kind of channel that we're still in. It's basically reacted from the top of that channel. But there's another kind of trend line here which connects these two peaks, which we're testing at the moment. I think the fact that it breathed through it so well was a bullish sign, but it's probably not gonna be, it wasn't much resistance in the way up, probably not in the much on the way down. We could get a drop through to around number 1,200. And then we've got the peak here at 190. But back through there, and it would take the edge off a bit of this bull run. This uptrend, you know, that could carry us all the way back down to 1,100 again. Maybe opening up the idea of a inverse head and shoulders, triple bottom type pattern. But I think we probably do need to hold this 1,190 to keep the momentum going.  That's it. Thank you for attending the webinar here. Apologies for the sound issues at the start. Hope that didn't affect you too much, but we're finishing a little early here. Try and keep it snappy. Thanks very much for attending and good luck with the trading this week.


I need eight and you have nine When you messed up one of your messed up say you messed up What are you gonna do now? See? Now do want to put brick around this eventually out see Hoppers this game as hoppers Top of the nether rack to make it a beacon. Yeah, I don't have any things fancy. She managed it yet. Oh, they have hoppers How do you hopper when did they do that? I'm behind man Don't tell me when I don't need to know when just I just I just don't know Is it a V or something iron in a small v-shape? Crap, I don't have any iron. So it's not a bucket. Isn't that a bucket though? Chest in the middle into a Y shape. Oh Okay, I need to I got to find more iron so warp Mesa for a Harden clay terracotta Okay, how do I can I warp home if I Don't go out there and be stranded if I warp out there. How do I get home? Set home, okay, okay Set home Here we go warp Mesa Get all of this chicken What's this how this work? What is that? What would that just pick up what what was that? Terracotta, how do I tip? What's a terracotta do? Oh god, okay? I thought I was gonna die. Hi What the how do I terracotta do I do I do I eat this do I burn it? I'm gonna burn it chat Let's see what burnt Terry. Yeah, let's see what burnt terracotta does wait. What happened to my wood? Oh whoa Glazed terracotta chat.  Maman a them clay. I'm gonna call them clay some more Orange terracotta What is this part? Is this a mod? This is vanilla. I never heard of terracotta Hakuna, my terracotta White terracotta is like a whole cake. I give you some tiramisu With all this terracotta All right Is there any clay around here though? You say a hardened clay So many so many recipes Which one's the hardened clay? What are you? No What's this? Red sand It's the same as the terracotta What do you mean like you think they've renamed it? Oh, so how can I convert this to clay? After you glaze it then what that was looking? I'm looking for clay man. What's clay?  So I gotta put another chest down. What did you give you smelt red sand?  I don't need to carry this wet man. Do I? No, I can do I can Well, thank you. Thank you for the iron sir Thank you for the iron. I Do have cold and I'm not using I'm just I don't know why I save it I'm just it's just been ingrained in my brain and just go for charcoal Yeah, so this This There we go pantaloonies. We got a full iron set of armor now You know pick click on that and Probably another axe at some point I need two picks actually. I don't have enough iron for that yet. I Will another pick ink three picks Well, remember all that wood I gathered we're about to use all of it chat for fuel I've got Minecraft Logging in every day Thanks for the 50 bits This is a bottom The bottom the original where is the original tunnel he's on all the cobble Well, we're bumming it digging holes. All you do is dig holes.    I'm taking my diamonds and I'm going home I'm dropping off my diamonds right now now Take my diamonds, and I'm going home Going home Going going going going home Got some gird More iron ore. Oh, please Sometimes I want to make double doors. Oh That might make one wall of a Of a brick you just go through you just go through that stuff so fast Clay that is All right, I run that one's empty. So what are you guys playing right now? Other than the ones playing Minecraft Monster Hunter Monster Hunter Final Fantasy 14. I never change. Oh, yeah, I played Monster Hunter this morning or this afternoon This morning morning. Yeah I didn't play that much though Play a little bit. I miss it not right now No, if I did if I didn't play this morning, I probably would have missed it, but I don't miss it that much So we got a little bit more iron I can make a shovel And an axe and my axe One more shovel Sword is good one stack of cobble. Please the rest can take a hike I will be playing Path of Exile next week For the dev league, I will be on that Playing your first scion cool I don't know. I'll probably doing a I've tried a bunch of different starter builds, but I might try something different this time. I might go with like Essence drain or I haven't done essence drain yet. I've done war chief told them I've done Um What's one day lastly I don't remember yeah, I'm probably gonna do essence drain this time. It's a little weird I think it takes a while to get going. That's what that's what turns me off of it Like it takes me a while. It'll probably take me a while to get going on. Why is that there? You know like this.   I don't remember That may 24 27 man That's nutty. Okay, so let's make some stone I'm gonna finish that roof.  Thanks for hanging out I don't remember half the things when that last play that I do remember those flicker strike bills He's the decent everything those are hilarious builds I think they're kind of still like that, but they're they're less spammy but Still kind of kind of crazy. This is like this, right? That's pressure plate. It's just three across. I think I have done every total builder is I'm quite convinced I have I need some ladders up here. Oh Naturally, I have spent all of my wood. Oh, that's what I did last season. I did uh, I did uh Which variant of arc did I do arc traps? Yeah, they are traps last season Because they buff they buffed arc and they buffed the traps and everything That's what I did.  It was so dumb.   Oh, that's what I did last season. I did arc traps This season is gonna be great. I can't wait. You know the thing I'm most excited for is not the delve not the whole end