Welcome back everyone. This will be our last video for lecture 35, which turned out to be on the little bit of the long side here We've seen previously How with a sequence there is no notion of tangent line, but we can still capture some ideas about optimization and monotonicity for sequences sometimes we can't borrow the derivative if the function can be Extended in a continuous differentiable way But we also seen that sometimes that the sequence approach can actually be more efficient I also in this in this video I want to demonstrate a technique which can be useful for computing the limit of a recursive sequence Because in this context recursive sequences might not have a natural extension to To a continuous or differentiable function and this is going to be based upon what's known as the monotone convergence theorem which basically says the following thing if we have a Bounded function, so there's some value on top that the function never surpasses and there's some value on the bottom that Again, the function never surpasses. We have some maximum value capital M and some minimum value little m I'm not saying the function actually touches these values But we know that it's bounded between these values it never gets above capital M It never gets below little m and also if the sequence is monotonic meaning it's it's always increasing Then the monotone convergence theorem says that the sequence must converge and the proof is basically the following illustration If you're bounded between these two values and your function is increasing It can go up up up up up up up up right, but there's sort of a limit, right? You can't just keep on going up forever your rate of increase kind of has to slow down with time And at some point you're going to taper off at some value and that value Is going to be the limit here So we get some living value so if the function is bounded and monotonic then it'll always always always be convergent So let's see an example why that might be useful. Let's investigate the sequence a sub in that's determined by the recursive Relationship that the base case is a one equals two So that's where it's going to start off and then we have the relationship that the next term of the sequence a n plus One will equal one half a n plus six whenever n is greater than equal to two So if you look at the first couple terms of the sequence, well, let's see those We'll build a chart here. So we have n and a n so one two three four five six That's oftentimes enough to see the pattern here. So it says it starts off at two So if we look at a two, we're gonna plug two into this machine right here You're gonna get two plus two plus six, which is an eight divide that by two You're gonna end up with a four Which is the next term in our sequence Record that here to find a three.  We'll do it just a few more terms if you do the seventh term Uh, that would give you 5.9 375 if you do the eighth term that's going to give you 5.9 6 8 7 5 and then lastly If you do the ninth term that would give you 5.9 8 4 3 7 5 So we can see that the initial term If we look at these first couple terms here, we can see that the term appears to be increasing It seems to be an increasing sequence and it seems like it's increasing toward The number six so we actually have sort of a conjecture that maybe Six is the limit of this sequence But how do we actually prove that because we've seen examples in in this course and also in In catechus one where a numerical estimate although helpful can be deceptive, right? How do we guarantee that the limit is in fact six? And so what we're going to do is we're going to use a technique that's referred to as mathematical induction It's a way of making sense out of patterns that are given by these limits or by these sequences Particularly how can we find the limit of this thing mathematical induction? So induction is a method we can use to prove things about sequences. It has three important parts to it So first there has to be some type of base case, right? We have to show that at some point The statement is true, right? So if we want to show that the sequence is increasing We have to be like, okay it increased it increased at some point And so for this one we could say something like a one Is smaller than a two notice here that a one What a one was in fact two, which is less than four So this is a base case that it starts off increasing great Then the next step But the next step here is what's often referred to as the inductive hypothesis The inductive hypothesis What we're going to do here is we're going to assume We're going to assume it holds assume the statement holds For a n So in that context what we mean here is that we're going to assume All right, so we did our base case for this. So we're trying to show that the sequence is increasing here So we showed the base case and so now what we're going to do is we're going to assume Assume that a n minus one is greater than a n and because the idea is if we if we showed One is less than two and then two is less than three and then three is less than four Four is less than five assume. We've got up to this point that a minus one. It will be less than a n okay And so then the third ingredient of our induction argument is We then have to establish the next case This is sometimes referred to as the inductive step We have to then thirdly we use the inductive hypothesis To show the statement holds For a n plus one the next term in the sequence. And so what we have to do is we have to then show That a n is less than a n plus one in our sequence And so we and we do this using the assumption that we had from before And so before we proceed in this in this I kind of want to give an analogy that imagine we're setting up a bunch of dominoes, right? We have a bunch of dominoes In a sequence like the so And maybe see something like this on youtube or something In order for a domino sequence to fall over and be some awesome display There's two ingredients basically first someone has to push the first domino over that's our base case from before But then also the dominoes have to be sufficiently close together so that when they fall They will knock the next one over And so that's what we're trying to do with this step right here That if we push this domino over it'll knock down the the next one in our sequence So for our sequence here, how do we show that it's increasing? Remember our recursive relationship Looks like a n plus one Is equal to one half A n plus six so we're gonna use this we're gonna use this statement to try to prove this and so we're gonna assume remember We're gonna assume That a n minus one is less than a n great So what we do is we're gonna start with this statement a n minus one is less than a n And so what we're gonna do is we're gonna add six to both sides This tells us that a n minus one plus six is less than a n plus six Alright, now we're going to times both sides by one half one half times a n minus one plus six is less than one half a n plus six now the right hand side One half a n minus one plus six that's equal to by this formula right here This is equal to a n and then the right hand side one half a n plus six like we see here This is equal to a n plus one and so we've been proven by induction That our sequence is is increasing See that wasn't so bad right we took our assumption and manipulated until we got the statement We wanted to and this proves that our dominoes fall over one by one by one towards infinity If we were to continue in this manner, so our sequence is an increasing sequence. We've now established that it's increasing by by Induction here, so that's an important thing to mention So if we were to switch the question up is our sequence bounded Is it bounded? Well, because it's increasing We know that a n is going to be greater than or equal to a sub zero I should say a one with the first term in our sequence, which is two So this gives us that it's bounded below because if you're if you're increasing you will always be bounded below That's automatic, but is it bounded above? That one's a little bit harder And again, we're going to use we're going to use induction to help us out here So for our the first the base case our can our following statement's going to be the following a one is less Which itself is equal to two is less than six Remember six was the number we think is the limit here And so we can then show that okay the first term of the sequence is bounded above by six The second step is we're going to assume Assume a n is less than or equal to six All right, so that was easy and the third step is we need to show That a n plus one is less than or equal to six And how we do that is typically taking the assumption we have before and manipulate it remember Kind of like we did it before a n is less than or equal to six. So let's add six to both sides Six plus six that's equals to 12 Times both sides by one half You get one half a n plus six Is less than or equal to 12 over two which is equal to six, but then the right hand the left hand side, excuse me This is just a n plus one And so this then establishes what we are looking for a n plus one is less than or equal to Six and so bobs your uncle there We've now shown that this function is in fact, it's bounded above it's bounded below Therefore this function the sequence is bounded And so why is this important remember how we started this video with the monotone convergence theorem by the monotone convergence theorem We see that the sequence a sub n Is convergent We see that the sequence is convergent that is to say that is a n has a limit Now it has a limit and we suspect that that limit Is six we our claim here is that still the limit is equal to six Now be aware that the monotone convergence theorem does not tell us what the limit is The monotone convergence theorem tells us that a limit exists And because the limit exists we still have to compute what it is now our claim is six And it's a pretty good claim and I want to show you What how how we actually prove it now so important observations the following following if we take the limit As in approaches infinity of a sub n this is equal to some limit value l This will also be the limit as in approaches infinity of a n plus one That is if we just start one term later in the sequence their end destination is still going to be the same thing And so we utilize that in the following calculation here Take the recursive sequence the recursive relation a n plus one is equal to one half A n plus six we are then going to take the limit as n goes to infinity on both sides So take the limit as n goes to infinity on the left and on the right Well on the left hand side it'll converge towards l whatever that limit is And by limit laws on the on the right hand side, we're going to get one half times the limit As n goes to infinity of a sub n and we're going to add six to that Which again the right hand side is going to become one half l plus six and so now we just want to solve this equation for l times both sides of the equation by two How we do this to cancel the one half on the left hand side a right hand side We get two l equals l plus six We're going to subtract l from both sides And then we can see exactly what we're looking for that this limit is equal to six So it's exactly what we claimed it to be Now when you look at this we look at this example here one might be Tempted might be very tempted to add to to to wonder Why did we have to go through all this process? I get how we took the limit of both sides on the recursive relationship And we were able to solve for the limit and get six and so that actually justifies why the limit was six along the way But one has to be very careful because this step right here Uh, if one's not careful could be done erroneously because when you're doing this step you take the limit of both sides You're assuming You're assuming That a sub n is convergent You're assuming a sub n is convergent Otherwise this calculation would be completely meaningless if the sequence wasn't convergent at all And so then assuming it's convergent you would drive this the limit has to be a six But what if the sequence is divergent if the sequence is divergent this this same equation would lead to six But the limit's not six if the sequence is divergent because the sequence Is divergent means the limit doesn't exist So this calculation is only valid if we know the sequence is convergent And the problem happens that there can be divergent sequences which are recursive That if you apply this idea of taking the limits of both sides You will end up with a number, but that's not the limit because it's divergent We can only do this calculation if we know the sequence is divergent And that's why the monotone convergence theorem was necessary And I wanted to mention this because there's a lot of kooky videos online on youtube for which people are Proving bizarre things like pi is equal to four or the harmonic series is equal to what is it supposed to equal to like Two thirds or negative three halves or something absurd like that. How are they getting How are they getting these completely false statements like the harmonic series, which is divergent? How could it possibly equal to a number it doesn't right the issue is they're they're using techniques for convergence theories on Divergent sequences and thus getting these erroneous any ridiculous statements then people are like, oh, it's magic No, it's not magic. It's just incorrect mathematics So in order so finding the limit of a recursive sequence is pretty easy because you just have to do this calculation But be aware this technique only works if the sequence is convergent If the sequence was divergent, we potentially could find a limit that is not correct So be cautious about those


We live in a time in which we've evolved over tens of thousands of years by learning from nature. That's why we are where we are. That's why we've achieved what we've achieved because we've been able to learn and we've been able to learn more rapidly than any other species, so we're more advanced. But the question is can we learn at an accelerated pace because we have to. The financial crisis was a big wake-up call. Our achievements, which have taken so long, are at risk. Our interconnectedness, globalization, is creating new interdependencies. And it's these interdependencies and our wealth that now creates unintended consequences, spillover effects, cascading amplifier domino effects, which, if we don't manage them more effectively, can set us all back. Pandemics, financial crises, cyber attacks, climate change. These are unintended consequences of our evolution, of our success. But can we go back to nature and ask the question how these links work? This is an example of our failure to do it. This is the derivative trades in the financial markets in the lead-up to the collapse of Lehman Brothers. And Lehman Brothers is the big ball at the bottom of this matrix. Everything was put in one basket. Too many resources were vested there. We didn't learn from nature. These are termite mounds on the Savannah landscape in Africa. Nature's learned to do things differently. It doesn't put all its eggs in one basket. It diversifies. It builds critical mass, but no one place is too big to fail. Pandemics are going to be perhaps the defining feature of how our interconnectedness overwhelms us. And we see that increasingly, and we see it in the Ebola outbreak in West Africa. Can we create ways to stop firebreaks, as well as ways to vaccinate, to stop it moving? And how do we manage our interconnectedness without this becoming a vulnerability? We've modeled, as shown here, that airline traffic exactly replicated the spread of swine flu in 160 countries in six weeks, with the big super spreaders being the big airports. We used to be in a different relationship with nature in harmony. And when we were poorer and there were fewer of us, this worked. But now we've become so wealthy and we have technologies and industrial level exploitation. It no longer does. That's why a tuner was auctioned for $1.8 million in Tokyo this year. This is why rhinoceros are becoming extinct and why the planet is becoming full. Governments also are not good. This is the Aral Sea. Six governments drawing water to feed their people doing the right thing collectively a disaster. So do we have the collective wisdom as well as the individual freedoms? And it's not just what we do to nature. It's increasingly also what nature is doing to us. The risks that it's posing are getting greater and it's poor people in poor places that are always most affected. So how can we learn from nature about how and where we settle? We need to ensure that the market alone does not drive decision making. But how do we get the prices right and how do we get the markets right? Left to their selves, rhinoceros will become extinct with horns worth more than gold. The tuner will disappear and the atmosphere will be filled. But we used to be able to live in harmony. These iconic polar bears drifting away on melting ice should be a wake-up call to us. We need to recognize the ability of the system to fall apart and our fragility. There's many different dimensions we can learn from nature. It's a complex web. The food, energy and other webs all interlink and so do our lives. What you do affects me and vice versa in new ways that amplify because we are wealthier. Because our choices affect each other. But do we recognize this and how do we recognize in a way that natural species do? The threads between us are thin. We need to regard them with great care. If this falls apart, if we cascade and amplify our risks, all our achievements will be nought. Civilizations that we've fought to develop will be set back. So it's a fragile planet. It's a planet where we have the opportunities of the most wonderful future that we could ever imagine. Free of poverty and disease. But it's also a possible disastrous future. So my question to all of you which I'd like to discuss is how can we learn from the way that natural systems do it to ensure we are able to manage our interdependencies and become more resilient. Thank you.


Sorry but I would just like to tell you how we set up anagios monitoring system at Strath-CLied to monitor our Moodle infrastructure and application. We have been running Moodle for 5 or 6 years now and with good uptime and it is really quite a stable system but we still have occasional problems when they're going to happen and what has happened so to do that we use this software Nagios we use a free open source version of it called core DIY Nagios has been around since 1999 so it's incredibly stable and mature and it looks like 1999 but that's another question. It enables monitoring of pretty much anything that you know you may want to to monitor in an IT system like network protocols, system resources, CPU, RAM, if you've got data sensors that have got things like probes or temperature sensors in them or anything it can monitor all that stuff so it's actually a really good system for for monitoring sort of the whole thing if you like and it does that by it runs on a server and monitors all the other servers and provides this kind of web front end for it which I'll show you later on. So the actual checks are done using plugins rather than being built into the software so there's a bit like Moodle there's about 50 core plugins that are actually shipped with the software they'll check all sorts of things and there's about 4,000 community created ones so it can check almost anything it's fantastic for that. So here's some examples just of the kind of thing that the plugins might return to you to tell you for example that your server's up and it's responding quickly or send me or isn't waiting to send any messages which is a problem we've had with our Moodle servers before or like your Apache services up. So some of these things like PING there's a a public interface but for things where there isn't a public interface where maybe a service is sitting behind a firewall or something like that we use this NADJOS remote plugin execution plugin essentially which just runs on the server to be monitored and securely passes the check data back to your NADJOS server so there's no need for security problems in your firewall or anything like that. So basically you just set up all the machines that you're monitoring be it servers or bits of IT hardware or whatever their hosts and you set up services which are things to be monitored within that host and NADJOS will give you these quite useful but not very pretty overview diagrams so the one on the top left is the very very high level it just shows you your system is kind of okay. The one on the bottom will show you each host and you know the status of it and the one at the top was every service the status of them individually. The reason it's really good for monitoring a Moodle service is because there are plugins for like all the kind of the bits that you would normally have in a Moodle set up like you know MySQL, Postgres and all that like Memcash D and the various different servers and it's also fairly easy to write your own plugins because it is just a shelf script to my colleague Michael I'm not sure if he's here wrote a plugin in a bit of an hour I think it was to to monitor end-to-end the Shibboleth login process using the B-hug testing framework actually and that that was like a really quick development but it was really useful so so I guess that's about infrastructure monitoring but we also wanted to monitor things within Moodle the application you know things like has the event cube become too big or has the cron job not run for long enough so what we did was we developed this plugin local Nagios which I think University of Kent also developed something similar but it allows it provides one single Nagios plugin check Moodle it's called and it will communicate with this plugin to do any check that you want it to do and pass the results back to Nagios. An example of where we've used this is like the events queue which we have a third party plugin that makes heavy use of that and it quite often gets blocked and it's a real nightmare to troubleshoot so we can now just monitor that and we say if the events queue gets beyond you know 100 events or something like let us know. Schedule tasks are another thing that are quite useful to monitor if you've got something that's like a really important schedule task and you expect it to run regularly you can get Nagios to let you know if it's maybe not run for an hour or something when you're expecting it to run every five minutes so instead of hard coding these checks into the plugin that we wrote we wrote a kind of a mini framework which allows any of the plugins we write to kind of expose anything as a service that can be monitored by by Nagios so you can then plug them straight into the application. Some successes we've had with this approach a couple of times we've been able to basically notice that shibboleth is down and get it fixed before anybody complained which is useful that's also an interesting one because we're monitoring somebody else's service it's not actually ours but we have to get it done. The events queue we've now got it so that we have a threshold set so if it gets beyond a certain level it'll warn us that you know that the events queue isn't working so we no longer have to notice that it's broken we can actually fix it really really quickly now so and what do you need to run Nagios basically you just need an old pc or an old server it's still kind of 1999 technology so it's all shell scripts and you don't need anything particularly major probably wouldn't run an apple too but the other thing you need is a bit of linux know how but actually probably not that much you just need to be able to write be able to write a shell script and that's really about it's got quite a high or a steep learning curve but it's also very very sort of simple at heart so that the theory of it is quite you know you always you're always well oriented because you know how it works so so that was a quick overview of how we use Nagios to monitor the application.


He's promised to speak here You know I went down to Miami and I'd ask him because he's a dating coach.   So what do you think about these guys? I'm trying to be politically correct.  No, I do not know you're very good at bringing out the worst It means that's why you're the president, right?    This is for real man.  I say she looks like a ninja turtle isn't my new favorite one Go look man. You it's funny.         There isn't an industry on the planet that has no frauds, right?   They hate it. They don't want to deal with it They're scared of it conflict is scary to them.  He's not one obviously He's all about it.   I Misled my audience about Devon's age, but I did that for privacy purposes. Dude listen man My results speak for themselves Speak for themselves Devon slept with a lot of guys gentlemen


7 Figure Trader Thoughts on Inflation. That is the number one metric that the Federal Reserve uses to determine the inflation. That's how they decide to raise or lower interest rates. At 8.30 a.m. market time, the CPI report is going to come out. If inflation comes in high, they have the opportunity to keep raising interest rates. If inflation comes in low, they might have the opportunity to reduce inflation. Now, the market is up like 20% this year, right? Obviously, we were fated 30% last year and stocks are rebounding. So I think whether the inflation report is good or bad, I think that's going to trigger some profit-taking, at least in the short term, for these stocks.


So, shall we start? What I'm bringing here, what I brought here is a synth kit by LittleBit and it's a, you know, small module to make synth either. What you can do with it is, you know, making your own musical instruments and play with it. So, but there is one big problem to, you know, introduce, no, not to have presentation. Do you like the band that talk a lot on stage? Maybe not. You know, maybe not. You know, I'm playing the music, but, you know, I don't like the band talk a lot. So, I want to start from, you know, playing. And I want your guy come closer and watch what I'm doing. And then you will know what it is. Okay? Come on, send out speakers, battery, oscillator. I'll use it. Can I turn it up a little bit? Oops. Once that finish, go home. Okay, so let's go back to your seat, please. Yeah. So you can make your musical instruments and you can play with it. So, you know, it's not new product, you know, it's very old product. I mean, I launch it, it was December 2013.  Yes.  Okay, good, good. So I just give you a short story, how I made it. The story is starting from 2012. 2012? Yeah. December 2012, email to little bit customer support. Because you know, I didn't have any contact with them.  There's a madam. My name is Tadahiko Sakamaki. I'm in charge of planning a co-inc. Cog is musical instruments company which produce traditional synthesizer keyboard on the unique music gear. Here you can check what you make. Well, you know, I've never, I've never checked it, you know, previously. I mean, this is my first time to read this email since I sent it to them. But it's crazy, you know. I'm so impressed by your product and I would love to discuss about it. What am I discussing? What am I discussing? Can I take your time for the purpose? I'm visiting New York from January 12th to our 17th. Thank you very much for inspiring me with such a fun and creative product. Best regards, Tadahiko. Thank you. Yeah, that was a very fast contact point, you know, between May and a little bit. And, you know, the reply was... Hello, Tadahiko. Thanks very much for writing in. We really appreciate your interest in a little bit. I'm going to ask around and see if this will be possible. We are, of course, familiar with Korg and are quite excited about your interest in us. So I, you know, contacted end of December and I met them in the middle of January. And I met the CEO and, you know, 12-up development manager. You know, I am Budel and Paul Hoffman. I think I have to show you the guy's name. So this is Aya, CEO. I'm not sure that I can find Paul Hoffman. Okay, so anyway, this is Aya Budel. And I had a meeting with her and Paul Hoffman and, you know, the meeting was not good. I mean, actually, you know, I thought, now I know it's totally wrong, but I thought passion is important. So I didn't prepare anything, you know. But if I, in the previous time thing, I thought I will lose some passion, you know. It's like reading something, you know. I have to explain what I want to do, what I want to do without any preparation. So I couldn't explain what I wanted to do at the meeting. But, you know, she and Paul Hoffman understand it very well, fortunately.  It's the reason why we could collaborate is not because of my passion. It's because of the reason why Paul Hoffman started art a little bit. And Paul Hoffman is the first employee of Little Bits. And when he started working at Little Bits, he asked Aya to allow him to do one thing. It was making synthesizer with, you know, Little Bits system.  And, you know, my presentation with Paul Hoffman did well. We started the, you know, project. And I had a meeting with Middles January. Then the, you know, I was in the business, you know, trouble in New York City. And I went back to Japan early February. And, you know, we started email, you know, email discussion with, you know, with them.  So, us, the Boca Loop guys use Maximus B. I use Maximus B as well. And I made the prototype of this module in one week, I think.  And, you know, I sent it to Paul Hoffman.  And he gave me some, you know, ideas and, you know, proposed out. And, you know, we, we updated the prototype, you know, in next one week. And then we decided the specification. So, all the specification has been done in, you know, three weeks or something, you know. And then we started the designing phase from early March.    So Paul Hoffman and one co-engineer started working on designing Turkey, you know, from early March. And then they are working on, they're working on, working on, I don't know the detail. And we had a launch, but we, okay, I think I should do a little bit more. I think they finished their hardware designing, you know, in May. And then we started making the manual, package, box, you know, bra, bra, bra, bra. And we got the first AR sample. It was like October, I think. And then we had a launch event in November. Then we, you know, started selling it in December. It was just one year since I sent the crazy, you know, crazy email. It was, you know, very first job and it was really a quick project. And where should I talk? I mean, it's for the designing and, you know, product development process.  It was like 15 people there. And when I, you know, visiting their office again for the launch event in New York, they became, I think, 30 or 40.  And the IR told me that since it helps a little bit a lot. And I'm not, it's still, it's true. But, you know, the IR told me that CNTGate was the most successful product for our little bit. And where should I talk more? I mean, I'm thinking about it. Yeah, I'm, yeah, they are, I'm, okay. So I'm explaining why I wanted to do a little bit. I'm, I'm working for Korg. And they are, Korg is a musical instruments company.  Yeah. It's pulled up like this. It's cool.  I like synth leather, but, you know, I don't want to be our synth geek.  Let's say normal people. Accessible? Accessible? Yes, that's right. Yeah, yeah. And the synth leather for the rest of us? Yeah, that's right. Yeah, yeah, yeah. So, um, um, but, you know, synth leather is, I think this one is simple. I think this has, you know, 30, not 30, 40 parameters.   It's got more than a thousand parameters. Yeah.  You know, they want to do more. They want to try more combinations. And I thought it is an issue.  But the synth gear needs a thousand. So, I thought that I have to, you know, feel the gap. I have to make the bridge between them. So, um, when I, you know, saw a little bit first time, I thought they solved the problem. Because, you know, it can connect and you can connect more and you can change the order, flexible, you know, more possibilities. So, I, you know, came up with the idea with making the synth with a little bit. So, the result is the combination of little bit module, which is in synth kit, synth kit has 13 or 14 modules. And for all combination possibilities, it was like, I don't really remember, but it's more than a million or two million. Yeah, it's more, it could be say that little bit has more parameters than this one, but it's simple at the same time. So, if you, if you only understand one parameters, just use one module, then you get this one, this sound. And if you understand, you know, another parameters, then connect it. You get a different sound. And if you understand another two parameters, connect it. So, you can, you know, use more module depending on how you understand synth data. And I had many workshops for kids, you know, with about the little bit, little bit synth kit. And the youngest attendee was, she was three years old, I think. She came to the workshop with his, you know, older brother, and he was six years old.  And, you know, she, three years old, they didn't join the workshop.  And then she started playing a little bit.  But she came to, you know, next to me and then pulled my clothes. And then she showed what she made. And she generally sounds like, you know, I don't remember, but. And then she looked at me and smiled. Then she made another sound. It was like, you know, maybe like this and smiled, you know.  Because, you know, I wanted to do it. I wanted to do, or I wanted to make synthesizer accessible. Yep.  You just connect it. And then if you get the sound you like, and then just smile it. This is the purpose. You don't have to understand everything. Okay. So, just, just try it after my presentation. Thank you very much.


Hello and welcome to a screencast about doing derivatives of quotients. So the quotient rule, hopefully you guys have been practicing the product rule because this rule is very similar with two major exceptions. So the first exception is obviously we have a fraction, okay? So that right here is the major exception. The other exception with the quotient rule is the negative sign in here. So that means the order that we do things in the numerator here does matter because obviously if you've ever balanced a checkbook, if you do 2 minus 3 or 3 minus 1, that's going to make a big difference in what you're doing. So the assumptions here are saying that f of x and g of x are differentiable functions that have derivatives f prime and g prime respectively. Their quotient q of x, which is written f of x over g of x, is also a differentiable function for all x where g of x cannot be zero, because g of x is in the denominator and we all know dominators can be zero. So q prime of x, the quotient rule is g of x times f prime minus f of x times g prime of x all over g of x squared. There are a few mnemonic devices that you may have heard before. You can look up if you want to. But like I said, the order of these really does matter. So I always start with the denominator and then I know to multiply by the derivative of the numerator. Then you do the numerator by the derivative of the denominator. So just as long as you remember which order to start in, you should be fine. Okay, our first example here in the direction, say, find the derivative of each function using proper notation. Our function we're given is b of x equals 3x to the 10th minus 4x to the 6, plus 15x minus pi all over x. So hopefully you can identify that this is a quotient. I'm just going to start by typing that quotient rule here. This obviously has a numerator and a denominator.  So since we want to practice a quotient rule, we're going to go ahead and do that. But I'm also going to show you how we can throw a little bit of algebra at this one and we could have made it even easier. Okay, so it just depends on what you prefer to do. If you want to practice a quotient rule or if you want to do algebra to simplify first, by all means, go ahead. Okay, so b prime of x. And let's go ahead and identify with these derivatives r before we get too far ahead. So if this is f, then f prime is going to be, well, this is, you know, you can look at this and it's got some sums and differences in here. I see, let's see, I see a power rule and then I also see a constant back here at the end, but we'll talk about that in a sec. Okay, so derivative of 3x squared is 30x to the 9th. The derivative, and that's because if you do 10 times 3, that gives us 30 and reduce your power by 1, that gives you a 9. Minus the derivative of 4x to the 6, multiply the 4 by the 6, we get 24, reduce our power by 1, that's going to give us x to the 5th. And then plus the derivative of 15x is 15. Pi's a constant, 3.14, blah, blah, blah. So when you do the derivative of that, that then ends up giving you 0. Okay, then the derivative of g prime, so the derivative of x is just 1, so g prime is just 1. Okay, so putting those pieces together then into our formula for the quotient rule, g of x, so that means we're going to take x, multiply it by f prime. So f prime is this polynomial that we found over here, 30x to the 9th minus 24x to the 5th plus 15 minus, okay. f, that was our original function in the numerator, 3x to the 10th minus 4x to the 6 plus 15x, oopsie, x, that was my x, minus pi times the derivative of our denominator, which was 1. And all of this big, crazy messiness here is all divided by the denominator squared. Okay, now to simplify things from here, this is just some algebra, so distribute your x through, multiply your negative through, combine your like terms, and then divide each piece by x squared, okay. Or, so this would be a perfectly legitimate answer. Or if you want to do some algebra, does anybody see how we could simplify b of x first? Well, if you remember, again, back to your algebra days, we can take each piece in our numerator and since we only have one piece in our denominator, we can divide each piece out. So b of x could actually look like, okay, so again, I'm going back to the original function. We're not going to look at those derivatives anymore. 3x to the 10th over x minus 4x to the 6 over x plus 15x over x minus pi. Okay? So is this any easier? I don't know, it just depends on how much you want to memorize the quotient rule. Now we will do an example where we're forced to use it soon enough, so don't worry about that. So when we work out the algebra here, let's see, that gives us 3x to the 9th minus 4x to the 5th plus 15. And then minus, now pi over x can't really be simplified, but remember, this looks kind of like a power, so we're going to want to bring that denominator up and go ahead and make that to the negative one power. So now b prime of x is going to give us, okay, apply the power rule to each piece. And remember these constants just get multiplied. So 3 times 9 gives us 27x to the 8th minus 4 times 5 gives me a 20x to the 4th plus, well let's see what happens to that 15. 15 is a constant, so that piece drops out. So then that one goes away. So we have minus pi times negative 1, so that's a positive pi, and then x to the negative 2, because negative 1 minus 2 gives us, or sorry, negative 1 minus 1 gives us negative 2, there we go. Okay, so this would also be a perfectly legitimate answer. So I leave it to the reader or the listener here to convince me, are these two answers actually the same? And the answer is yes. It's just you took two different ways in order to figure out what this derivative is, and if that confuses you, then just pick whichever way makes more sense to you. But again, I prefer to kind of go with the second route, because to me, these derivatives are a lot easier than trying to remember what the quotient rule is. Okay, fantastic. But now I come to a function here, v of t, that's 3t minus 2t to the fourth plus the square root of t, all over t squared minus seven. So our little trick on that last example will not work with this one. You cannot break up each piece just because how the vision works, okay? So that just isn't possible. So for this one, we're gonna call the numerator f and the denominator g. So let's go ahead and figure out what the derivatives are for each of these. So f prime is, you notice I threw a, what's the first piece here? Exponential, right? So what's the derivative of 3 to the t? Well, that's 3 to the t times the natural log of 3 minus, what's the derivative of 2t to the fourth? That would be 8t to the third, because 2 times 4 gives me the 8 in front. Drop my power down by 1, that gives me a 3. Plus, okay, the square root of t, remember that's t to the 1 half power. So then the derivative of t to the 1 half is 1 half t to the negative 1 half. Cuz drop that 1 half down front, technically we multiply by 1. Then 1 half minus 1, well it's 1 half minus 2 half, gives me a negative 1 half. Okay, then g, the derivative, or the denominator here, that's t squared minus 7, that derivative is just 2t. Because we bring the 2 down front and then reduce that power by 1, that gives us a 1 technically. And then minus 7, that drops out because of the fact that it's a constant. So that one goes away. Okay, so now let's go ahead and write out that quotient rule again. So which one do we start with again? We start with the denominator.  Okay, so this is a little bit of a shortcut way to write it, similar to how I put it up above. Okay, so now let's go ahead and put those pieces together. So g of x or g of t in this case, so that's my denominator. So in this case, that's t squared minus 7 times f prime. So that's all this junk we found up here in the numerator for the derivative. So 3 to the t ln of 3 minus 8t cubed plus 1 half t to the negative 1 half minus, okay, f, so that was my original function in my numerator. 3 to the t, oopsie, minus 2t to the fourth plus the square root of t. And then times the derivative of my denominator, which was 2t. And all of this junk is divided by the original denominator, t squared minus 7 squared. And that is your answer. Now, again, depending on what your instructor expects out of you, you may have to multiply some of this stuff out, but that's algebra. I'll leave that one to the listener. Thank you for watching.


Yeah. Okay, good. I'm looking for some information on the projected growth of the fitness industry over the next five years. I can help you with that. Perfect. Let's go over here and get an iPad.


okay this is James P. Madonna from the Facebook group everything is food I have arrived for my Friday lunch buffet there's a new farmers market that opened up right after the 24-hour fitness center and I'm not sure if you can make it out it says grand opening very clean oh it seems to be owned by Indians it's very shockingly clean but the prices are high I was in there a few times already but but a very clean impressive place here you have the my favorite dollar store the dollar zone right the dollar zone all right Commodore Jeff Zambello the dollar zone and I'm going to get out of the car and head for the buffet as the dollars on don't mind me I'm just drinking some coffee that I had at home coffee to go strong coffee to go unlike that weak garbage they sell at McDonald's or possibly Burger King but I haven't had Burger King coffee in a long time or Wendy's coffee you Gebronies now I am going to expedite the car this is the beginning of a heatwave oh over 90 degrees today right not good it's gonna be that way all week excuse me I digress all right of course I will hit the dollar zone after the buffet see what the hell what's going on here I tell these Gebronies don't put the bamboo near the window they like low light bright light turns the bamboo yellow and they die but do they listen to me no they don't fucking listen to me white as fucking as there's a Walmart and overpriced rip-off Moldell's boarding goods bastards beauty supply store all right all right let's see how many people show up there's Frank's pizza very popular place here cricket forget it rip-off cricket wireless screwed on expensive all right I am now entering these Gebronies let's see if it's crowded or not all right here we go the Royal Hibachi buffet I am entering it right now here we got some amusements I'm entering it right now technically it's not phase one but see what we got going here oh well not too crowded all right James being Madonna phase one Royal Hibachi grill it's Friday afternoon lunchtime Royal Hibachi grill buffet Facebook group everything is food let's see what's going on whoa wait a minute hmm you know what this is interesting let me double-check and see what's over here see we got the steak and onions no lamb oh boy the flounder is very good the flounder is very good here but you know what you know what being that they got the hardcore sushi well semi hardcore I might as well take advantage I'll take advantage of it I think I think that's the white tuna all right I'll take some of that right I better make sure it's a white tuna some octopus hey it's a white tuna right or tilapia white tuna good all right that's it whoops okay we got octopus white tuna let me get some I'm gonna show it no I thought that was an odd look at some of this spicy tuna roll spicy tuna roll here's some raw squid on here raw squid sashimi I'm doing it I'm doing an ass backwards because I want to take advantage of the fact that they have some good pieces of sushi all right little pickled ginger Commodore Jeff Sanbella you know about pickled ginger right it looks like strips of kosher of pastrami I could get you know what let me let me grab a piece of flounder even though it's gonna hey look what's going on here the beautiful imported lamb fictions from turkey are lit aren't they beautiful look at that no American light fixtures like this none none whatsoever all right where was I I digressed I digress get some nice flounder fillet flounder fillet that big it's huge look at this look at this unbelievable look at this I never see I never seen a flounder fillet look at this brand this thick look at that look at that you're brawnies catch you today fresh flounder look at that Royal Hibachi buffet we're 46 West out of New Jersey right maybe I'll take that I'll leave the rest for the rest of the customer I'll be generous I'll be generous there ain't no lamb but all right now I think with the duck situation I'm getting tired of getting all greased up and if there's any out later I'll probably grab some nice crawdads okay let me get some soy sauce mixed with the wasabi for dipping fine art of dipping sushi and sashimi this over here that's like I got so much in on here for a second oh my god what a jabroni I made a spell I shouldn't have that wasn't nice to me I don't see anything I could wipe it with but I will come back and fix the situation all right let me put this back let me go to my table we go to my table and I'll get the lemons like I normally do octopus spicy tuna roll very thick fresh flounder fillet calamari sashimi and white tuna sashimi now I want to show you what a nice guy I am I'm not like these other customers okay I'm gonna return and I'm going to wipe up my mess see nobody else does this I clean up my my mess the only customer in the world that everybody else forget it they don't care you still probably have to wipe it there you go look your liberty why you want me to clean more all right the lemons I won't bore you with look at it not too crowded see how see how conscientious I am get your bronies all right this is what I normally do as everyone knows I mixed the wasabi in with the sui sauce so I mean the soy sauce and I keep on I keep on stirring slowly until it mixes and then I use this as a dipping sauce look what I just did son of a bitch unbelievable unbelievable the evil spirits of I'll follow me on this first day of the heatwave I never do this I never do it how dare how dare I spill anything and make a mess oh my god it's really upset me when I make a mess all right where was I before it was really interrupted stir it up well you know what let me get to that let me get to that I don't want to digress too much I'm going to do my lemons for ice lemon water the most refreshing healthy drink or one of known to mankind and that will be in a moment as you can see fork inside of lemon wedge and squeeze hard and that's how I squeeze lemons and limes okay and that I will continue to put several in the glass until I have my homemade lemonade of course I hold the other end of the fork but you know naturally I can't do that right now what a depressing song this is can't live anymore living living without you can't live any more oh my god all right no lamb there's a great plan this looks interesting sauce shrimp cherry stone clams and mussels some kind of white sauce which I will find out soon enough take a cup do one more kind of like a French style bouillabaisse right change pink Madonna Facebook group everything is food a white Commodore Jeff Zanbella before I had catch of the day even larger fresh flounder this front flounder filet is even larger than it was last week excellent I'll have this see if they got any bodies out dry calamari fry calamari bodies oh look at this looks like a coconut battered shrimp according to the rough texture you know I don't want people to think I'm talking to myself all right looks like coconut okay yellow squash zucchini and grill a grilled cauliflower or grilled very nice very nice it's some yellow squash much room really when you think about it we got another yellow squash a road piece of cold grilled cauliflower you know what I don't have any more room and notice they've got the French toast often I gotta give it a shot it's got the syrup on it and everything I gotta try a couple pieces you know maybe fair maybe for dessert if they don't put out anything that I really like wow look at that chocolate cake how dark it is it's very nice I'll be busy enough with this this pile of King Neptune's delights okay I was gonna get high screen but until I saw more um white tuna come out octopus and squid actually everything came out just a batter oh look at that Kim Chi Kim Chi blessed their heart Kim Chi I'm gonna definitely gonna get white tuna no doubt about that I'll get a little bit I don't want to deplete their stock you know all right that's enough I could take the whole friggin tray actually do I want some Kim Chi sure cabbage is highly nutritious one of the top nutritious vegetables known up there next to watercress I can't get that open screw it oh I hear happy birthday some kids birthday the hell is that Michael Jackson singing happy birthday the Jeff Zambello look with your stringy kosher pastrami disguised as pickle ginger like Michael Jackson singing happy birthday to one of the little boys they used to share his bed this isn't bad spiced tuna that's enough for me I don't see any onagi I think I'm not gonna dip this in soy sauce and wasabi I want to enjoy the beautiful flavor of white tuna see if they got any lamb out no lamb what whiting oh they took the flounder away too bad white eh whiting is it's all right it's all right whiting is all right try that coconut shrimp it's real good on the other side you can you get busy though anyway I notice huh that's right I was gonna try french toast oh look at that red peppers roasted roasted red peppers interesting you know what as good as it looks I think I'm gonna pass calamari rings I'm not in a mood this week he was latinos maduros coconut shrimp very tasty but I had enough look at that the real grape leaves are going out there I'm not in a mood for that either roasted red peppers it's interesting is they finally got the flashing LED lights to work on the ice cream station the ice cream station they got it fixed last week look at how beautiful that is it's changing colors look at it look at it unbelievable you gotta love technology you gotta love it look at that different colors beautiful all right I'll take one should I take another one now you know what let me let me try one for now and then most likely I'll probably hit the ice cream next ice cream there it is different flashing colors hard ice cream oh look at that they put on new tubs put on new tubs there we go beautiful beautiful much gemron is unbelievable ice cream it's got so busy it's so busy man it's incredible here at the Royal Apache buffet that's an odd combination but it will do for now the next it will be ice cream which is right there kimchi white tuna sashimi and a roasted red pepper look how busy look how busy my ice cream station is look how busy the ice cream station is oh my god and I hope that line is not there when I'm ready they just put out new new fresh tubs of ice cream well will they be there when I get there that's the question gotten so busy usually when it's hot and and and and sunny and clear usually everybody's outdoors apparently not not today here oh my god oh yeah before you know what those new tubs of ice cream will be gone the way these kids are attacking it unbelievable unbelievable unbelievable well I'm gonna I'm gonna go soon so I hope that they left enough ice cream for me hard ice cream man well this is it ice cream ice cream ice cream station of Royal Apache buffet rule 46 west out of booking Jersey and I am going to have some strawberry ice cream like I didn't see any small dessert spoon so I'm gonna have I'm gonna have to use the large soup spoon which I didn't use so it's technically clean because I didn't have any soup and that's that folks got busy really got busy this afternoon it is the end of June 2018 and this I believe this Sunday is July 1st 2018 so it is the end of the month it is Friday afternoon look at this no wonder no wonder the ice cream doesn't have a chance to get hard the doors always swinging open all these kids diving right into it the ice the strawberry ice cream is vanishing there's a little boys been crying for a while disappearing Royal Apache buffet rule 46 west out of booking Jersey right next to Walmart 24-hour fitness actually in between and next to the dollar zone why why why why why why why why why he's so upset he's at the greatest buffet I know of one of at least yeah I have no idea why he's carrying on why why sounds like the people on social media on Facebook when their feelings get hurt you know when somebody posts a comment and it hits a raw nerve something that they don't want to hear like reality they start crying like that too when it's gone I told you that giant mountain of strawberry ice cream will be gone I told you I guarantee James be Madonna gamma routine oh gotta love it gotta love it I definitely lost money with me that's for sure I did gone see how conscious I am I leave up a little placemat so I don't make a mess how many Americans do that how many Americans do that how many Americans do that I'm the only one just like when I go to all these when I go shopping I lay out I lay out the barriers you know nobody does that let me finish up my lemon water well that's it for me guys till next time jace be Madonna saying have an invigorating week and weekend and a safe one too actually next holiday will be 4th of July weekend that's right what the July weekend in the United States have a good one there's the busy ice cream station got a long wait man a long wait I don't know what happened today see what happens


Hello everybody, welcome back to the second channel. Take a look at these Greg pillows, dude. We got Greg pillows. Greg pillows in the background. You guys thought I didn't want Greg letters in the background anymore.  Thank you to HelpfulMig on TikTok for making these pillows. They fit the couch perfectly in all honesty. I'm really stoked about those pillows. So thank you for making them HelpfulMig and I hope you guys liked them. Anyway, welcome back to the second channel. Today we're going to be talking about some of the weirdest YouTube shorts that I could find on YouTube. So crack open a sparkling water and we'll crack into these TikTok or YouTube shorts. YouTube has been pushing YouTube shorts like crazy. I'm kind of curious to know if anybody who watches this like watches YouTube shorts. Now I'm not trying to be judgy in any way. I'm just like, I'm just curious because they're pushing them so much to see if it's actually working. I was going through YouTube's list of the top 500 YouTubers over the past 30 days. And if you click on like half of these channels, they only post YouTube shorts. So like all of the people that are being subscribed to the most right now are like just YouTube shorts channel.  They want, they're like, you will watch YouTube shorts instead of TikTok. But because YouTube is just kind of like pushing anybody that posts YouTube shorts, there's a lot of weird channels that end up doing really well on YouTube now just cause they're like one of the few that are just cranking out YouTube shorts and posting them on YouTube. So I just scrolled down this list of like the top YouTubers over the past 30 days and I clicked on some of them that just post YouTube shorts. So let's get into it. First of all, these folks called MoniLena now have 6.5 million subscribers. They created their channel in May of last year and they already have 6 million subscribers. That's how hard YouTube is pushing YouTube shorts. So let's go ahead and check out some of their TikToks and find out like, is YouTube's heavy endorsement of YouTube shorts paying off with some quality content? My voice did not crack.  What did she think was gonna happen? She's like, okay, I'm eating ice cream and my husband is handcuffing me. And then she gets handcuffed and she's like, wait, now I can't move my arms independently of each other.  How did you do this? You wizard. You tricked me. She could have moved her hands away if she wanted to. That didn't restrict her from moving her arms at all. She could have just gone like this and been like, no.  So he could have just done that without tying her up first. I guess his aim was to humiliate her and then take her ice cream. Is this an ad for this ice cream? Why is this laying out like this? I don't know about you guys but I'm about to freaking fly to Russia and buy one of these because I'm being advertised to so hard. Is this Russian? We'll never know. OMG left without candies. Okay, so the guy's moving around the bucket. She's got to pick which one has the lollipop in it. She picked the wrong one because that one doesn't have the lollipop in it. And it has actually more than the lollipop in it. Oh, so he's a magician in this one too. Are all of their TikToks just about the guy being the most clever guy in the world and the girl being the dumbest girl in the world?   OMG, you can't joke with your wife. Is this TikTok about to be about like cancel culture? What, you can't even joke with your own wife anymore?  You're not even allowed to joke with your wife anymore?  People are so PC these days. Oh no, he hits her.  As a joke, I did it. And then she hits back.  The lady is cute and good looking.  Cause I think I have an interested party here. I am done, dude. I am done joking with my wife via flip-flop violence. Okay, well you know what? She actually seems to be the clever one in this TikTok so I guess they do kind of go back and forth. Sometimes the guy has a hundred IQ points on his wife and sometimes it's the other way around. Sometimes it is the guy getting slapped with the cucumber. That age old saying, one interesting thing about YouTube shorts is that when you click on one and then you scroll, it just starts playing random shit that you're not interested in at all. Okay, that guy's actually magic.  How did he do that? Dan Rhodes. Okay, I was actually kind of expecting to see a TikTok that didn't interest me at all, but this one actually did pique my curiosity. I think there's a little divider in there. You can see this little part of the cup straight line right here. I think that's dividing and there was juice hiding behind that. That's my little theory about this one. But apparently a really big format on TikTok is to do something amazing near a girl and she's gonna be mad impressed and you're kind of like, yeah, I just do that. I just do stuff like that. I actually didn't expect that to happen. I don't know how I did that. So is this a cat trying out viral life hacks or something? I don't guess it's not a life hack. How to make a squishy carrot, you know? You always want to do that, but it takes forever. Here's sort of a DIY way, DIY life hack way to do it. Okay, but the cat is clearly pouring in coke and it's said to do Pepsi. So actually, we're not sure if this one works. What a strange idea for a YouTube channel. That little pup, he just tries out viral things. I don't even know how to classify these. Life hack crafts, they're just like things that you can do. Viral things that you didn't know you could do. And also that you can't do. It doesn't work. The people who make these videos must have like little fake cat pots that they use to do all this stuff with. That's kind of strange. I mean, I guess more power to them. They're probably literally raking it in because they make YouTube short. Yeah, they've got 10 billion subscribers and this cat is basically a celebrity now. Okay, back to Moni Lena, the Mona Lisa. OMG, he thought the snake was his wife. Okay, that went a different direction than I thought. I thought it was gonna be a prank where he wakes up and gets scared by the snake. Maybe that's what the wife was expecting too.  You're supposed to realize it's not me. I'm not a snake. And the husband's like, I love my wife. My wife who is as thin as my wrists and covered in scales and slimy and biting me all the time. I love my little wife who hisses at me.  The whole family is master in pranking each other after seeing their all videos. Conclusion, their daughter will be a great prankster in the future due to genes of parents.  How do you know that? I'm a doctor in the chat already diagnosing their daughter with being a genetically pure prankster. Have scientists figured out yet if being a good prankster is genetic or is that like a learned behavior? I think they're still trying to figure that out actually. I think that's kind of, I think that's a big field of study right now. Let's maybe look at like one of their most viewed videos. Oh my God, dude, 280 million views, 160 million views. They have so many videos with over 100 million views. OMG, P prank with shaving foam. What do you mean P prank?  Or is that just a typo, like a little stutter?  They're so scared while writing it with shaving foam. Moinika, the fuck? Okay, for one, he looked directly into the barrel and there's no possible way you could have missed a white speck in the barrel unless you're incredibly behind. So I would put this as stage. Well done, Enzo, you figured it out. I feel like I said this in the last video I did about YouTube shorts, but it does make me wonder, are we supposed to think it's real Is this just like a funny scenario and even if we don't think it's real it can still be it can still be kind of funny Cuz like I mean like you can go watch a movie that's funny And you know it's not real and it can still be funny And I'm just explaining the concept of fiction to everybody at home, but you know, you know, I mean you know what I mean I mean, maybe it's just like tiny teeny tiny little kids watching these videos And so they're like yes, this is probably real everything else I've experienced in life has led me to believe this is real My parents are real my friends are real everything is everything I've ever seen is real lose clues is real So I don't see any reason why this would be The fact that they added a laugh track into this one. It really says a lot I think honestly about their process and making this video.  It's actually just like a weird unsettling video Do you think we should try to add in some kind of indication that it's supposed to be funny And so they just added people laughing in the background. It's funny. It's okay. We're fine mentally Okay, so you don't have to worry about it. It's funny. I'm washing his jacket. Most of the comments on this video are just like spam in Dot-coms dot date. That's my new favorite dating website, you know before I was really into e harmony dot-com match dot-com Christian mingle dot-com now. I'm more into in dot-coms dot date Son Uno's Delos in dot-coms dot date I kind of want to click on it just to see what it is, but I know the second I do my computer is going to explode with a virus someone responded. Okay. All right, buddy sure You are my favorite loves dot-com dot date. YouTube has an insane spam problem Can we talk about that?  Just don't just make it so they can't do that and also maybe I mean if you are maybe just like banned words like come and Slut in the comments. I mean is that is it that is that hard? All right? Anyway enough about that Let's get back to the YouTube shorts I found another channel called small and for a second. I was like this kind of look like Troom-Troom videos so I clicked on the channels to see if they were associated with Troom-Troom And they are actually associated with a channel called Bada boom not Troom-Troom I am a little bit suspicious that Bada boom is also owned by Troom-Troom, but there's no mention of that anywhere But just like the aesthetic of their videos look very Troom-Troom-esque, so I'm not gonna rule it out that anyway Let's check out some of smalls YouTube shorts Let's go straight for most popular helping others is important mobile game ads be like and this also has 200 million views This is like an insanely well produced version of those videos that I made a video about a Drew and Curtis But these ones actually look very well produced and well animated I'm also noticing that the last YouTube channel we're looking at had like 90 comments on some videos And this one has like a similar amount of views and has almost 6,000 comments That's a little bit odd weird ways to sneak food into the movies and not get caught edible hair I'll give it to him. That is a weird way to sneak food into the movies You know like how you go into a movie. It's like a club slash airport. That's what the movie theater is Also is that one to candy detector?   They're in a club But then why didn't they just make the title weird ways to sneak food into a dance party? Maybe they filmed this and then they were about to post it with that title But they were like wait you actually can just bring a snack into a dance party if you want to that doesn't make Why would you need to sneak food into a dance party and so they changed it to the movies honestly even though you can bring Food to a dance party this still is a weird way to sneak food into a dance party It actually makes it weirder that you don't have to sneak it in the fact that you could just bring the food and instead you Like made a wig out of twizzlers or whatever you were like no now Nobody's gonna know nobody's gonna know when they brush up against me And I'm sticky and smell like strawberries that my head my whole hair is made out of candy Oh now it's gonna show us how to do it. I think I figured it out I think you kind of put it on your head and you put a hat on and then you've got candy for hair amazing balloon trick number four Little too excited about that water balloon Not necessary I'm so on the edge of my seat dude. What is this amazing trick gonna be is it just that he built it up that much? That is pretty cool That's amazing Okay, that actually is pretty sick the slow-mo shot was cool. I'll give them now I just thought it was gonna be like a trick shot imagine if dude perfect videos were like this They're like basketball trick shots and it's just them throwing the basketball off of a large thing onto the ground And it just hits the ground whoa gravity still works. That's awesome I was worried that we're gonna stop doing that upside down prank dude This channel is all over the place dude. They know what types of videos they make what is the description of this channel? Say actually hello everybody We are short funny and humorous videos on a variety of topics you can say that again if you like magic tricks pranks Lifehacks vines challenges ASMR and much more than join us We will not let you get bored be sure we will not let you get bored if we even sense you starting to get bored from one of our videos We're gonna come over there strap you to your chair We're gonna handcuff you with a belt and we're gonna entertain you with some amazing water balloon tricks Okay, it looks like just a normal guy hanging out a guy with the baddest hog known to man mind you also Did you see his hands were feet they really tried to hide those by putting them behind his head But you could just see one sticking out like this and it was a foot the girl comes in She's like yo dad me up and it's just a foot That'd be funny act that would be funny this prank is funny And what is going on here? What is this? This is very interesting.  All right. Thank you for watching Bye-bye


Here's the outline of a program we want to write. It asks a yes or no question and processes the user's response. What you see here is called pseudocode. It's part English, part Java. In order to write this program, we need to learn how to read strings for input and how to get the first letter of the string so that we can compare it against the why for yes and n for no. To read a string from the keyboard, you use the next line method as shown here. It reads everything up to the next new line, which was provided when you pressed the Enter key. The book also mentions the next method, which reads up to the next whitespace character. This is useful for reading input one word at a time. Once we have the string, we need to get the first character. To get a specific character from a string, we use the charAt method and give an index number that tells which character we want. The first character in a string has an index number of zero, not number one. For this string, welcome to Java. Calling charAt zero for the message gives back the letter w. CharAt five of the message gives us back the letter m. And if we go beyond the end of the string, Java gives a runtime error. Notice that 15 is out of bounds. Even though there are 15 characters in the string, they're numbered zero through 14. Our last valid index number is 14, not 15. This is a source of many errors when people are just starting out losing strings in Java, by the way. Now that we know this, let's put it together into our program. We prompt the user and read the next line of input into a string. Sometimes users will enter an extra blank before they start their answer, especially if your cursor is too close to the prompt. So we'll use trim to get rid of the spaces and put that back into our answer variable. We're looking for an uppercase y for yes and an uppercase n for no. So we'll convert our answer to uppercase and reassign that to answer. Now we need the first letter. We take the character at index zero of the answer and assign it to a variable named yes or no. If that character is a capital Y, we print out one response. Otherwise, if that letter was a capital N, we print a different response. Otherwise, it's not either a yes or a no, a Y or an N, and we print out this response. Let's run this program several times to see it in action. If we type a capital Y, we get the yes response. Let's put some spaces in and type the word nope, which begins with the letter N, and we get that response. And if we put in something like I don't know, we get the response that the answer wasn't understood. And that's our program that reads strings from the keyboard and uses the char at method to extract specific characters from that string.