1. ## Help (Parametric Equation)

Ok so my teacher taught us how to do this but now for a question like this. Can someone tell me how to go about this question?

Find the parametric equations for the surface obtained by rotating the curve y=e^-x, 0 less than or equal to y less than or equal to 2, about the x axis. Thanks again for the help..this site is so helpful!

2. Let $f(x)=e^{-x}$

First paramaterize the x-direction with just x. Now consider the y and z as just circles in the y-z plane. The equation for y and z would then be:

$y=f(x)\cos(t)$

$z=f(x)\sin(t)$

Then the parameterization for the surface of revolution would be:

$\{x,f(x)\cos(t),f(x)\sin(t)\},\quad 0\leq t \leq 2\pi$

and x whatever range you wish.