Calc Help, Please! 2 Problems.

Test Preparation
1

<p>Wondering if some Calc students/experts could help me out with these two problems that I'm having trouble with. They deal with rates of change, which I've realized, I don't understand quite well. </p>

<p>A radius of a right cylinder is given by (t +2)^1/2 and its height is ½ ((t)^1/2) where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume with respect to time. </p>

<p>Determine whether there exists any values of x in the interval [0,2 pi) such that the rate of change of f(x) = sec x and the rate of change of g(x) = csc x are equal. </p>

<p>Thank you so much! Steps leading to the answer would be very helpful.</p>

2

<p>'Rate of change' is just dV/dt for the cylinder problem (rate of change of volume versus time), where V = cylinder volume. </p>

<p>For the trig problem, the rates of change are df/dx and dg/dx respectively.</p>

3

<p>V = (pi)(r^2)h
r = (t+2)^1/2
h = ½ ((t)^1/2)</p>

<p>V = (pi) ((t+2)^1/2)^2)(1/2)(t^1/2)
= (pi)(t+2)(1/2)(t^1/2)
= (pi/2)(t+2)(t^1/2)
= (pi/2)(t^3/2+2t^1/2)</p>

<p>dV/dt = (pi/2)[(3/2)(t^1/2)+t^-1/2]</p>

<p>I think that's right. Even if it's not, you get the general idea.</p>