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Rate of Change of Clock Hands [08/11/1999]
The minute hand on a watch is 8 mm long and the hour hand is 4 mm long. How fast is the distance between the tips of the hands changing at one o'clock?

A Reduction Formula and a Special Method [1/23/1996]
Asking for the integration of F(X).

Related Rates [10/16/2003]


Relativity [05/22/2002]

Riemann Sums as Estimates of Definite Integral [10/11/2003]
The velocity of a car is given by v(t) = t^2 + 2t where v(t) is measured in ft/sec and t is measured in seconds. Estimate the distance traveled from t=1 to t=4 using 3 subdivisions. How accurate is this estimate?

Rocket Position and Velocity [04/12/2001]

Rope between Two Poles [05/04/1999]
Show that the shortest length of rope occurs when angle PRQ = angle SRT.

Salt Concentration [01/23/1997]
One tank contains fresh water while another contains a salt solution. If the contents of each tank are pumped into the other tank, what is the concentration of salt in each tank at any time?

Shortest Distance Between Two Vectors [04/07/1998]
How do you find the shortest distance between two 3-dimensional lines?

Simpson's Rule for Cubics [10/23/2000]
Why is Simpson's rule exact for cubic polynomials?

Sinusoidal Output of Electronic Oscillators [04/28/2005]
Why does an electronic oscillator oscillate in a sinusoidal wave shape when electronic devices work in a linear region?


Snail! [06/20/2002]

Solving a Differential Equation [6/5/1996]

Solving a Differential Equation by Series [06/13/1999]
How can I solve y' = 2xy by series?

Solving Double Integrals Using Symmetry [11/05/2004]
I'm very curious to learn how symmetry could be used to solve double integrals such as z = e^(x^2) - e^(y^2) over the domain [0,1] x [0,1]. I've heard that the method allows you to solve such problems quickly.


Solving for the Non-homogeneous Equation [10/21/2001]
I have the equation: x^2(d^2y/dx^2) - 3x(dy/dx) = 3x^3. How do I solve for the non-homogeneous equation?

Solving Functional Equations [08/11/2005]


Standard Deviation of Uniform Distribution [02/16/1998]
In the equation Std. deviation = (b-a)/ square root of 12, where did the square root of 12 come from?


Stationary Point [10/27/1999]


Substituting y = vx in Differential Equations [02/16/2001]
How can I make the equation (y^2 - x^2)dy + 2xy*dx = 0 separable?

Summation Formulas for Trigonometric Functions [04/24/2001]

Surface Area and Volume Derivative [10/30/2000]

Surface Area of an Ellipsoid [02/11/1997]
How do you calculate the surface area of an ellipsoid?



Surface Area of a Sphere [10/03/1997]

Surface Area of a Sphere [04/10/1998]


Surface Integrals of Vector Calculus [01/05/1999]
Find the SURFACE_INT(F dS) of the vector field F = (x^3, y^3, z^3) through the surface of the solid circular cylinder...

Tangent Lines and Odd Degree Polynomials [07/24/1998]
If p(x) is a polynomial of odd degree, determine whether every point in the plane lies on at least one line tangent to the curve y = p(x).


Taylor Series Expansion [11/24/2001]

Tensor Calculus [03/06/1998]
Scalars, vectors, and tensors, and their components.

Tensor Calculus [10/10/2002]
Could you please remind me of the general definition of a determinant for a tensor with more than 2 indices, like T_m1_m2..._mk ?


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