1. Use the chain rule to find dz/ds where z=3x ln(y) x=s cos(t) y=2s sin(t) Your

Question

1. Use the chain rule to find dz/ds where

z=3x ln(y)

x=s cos(t)

y=2s sin(t)

Your final answer should depend on s and t only

2. Let S be the surface given by the equation

xy+xz+yz=0

and let P be the point (1,2,-2/3)

(a) Find the equation of the tangent plane of S at P

(b)Find a parametric equation for the normal line to S at P. (The normal line is the line perpendicular to S at P that also goes through P.)

3. A wedge-like region E is cu from he parabolic cylinder y=2x^2 by the planes z=0 and 2y+2z=1. Set up a triple integral representing the volume of E with order of integration ??? dz dy dx

and appropriate integration limits for each variable. DON'T EVALUATE THE INTEGRAL

Explanation / Answer

1)

dz/ds=(dz/dx)(dx/ds)+(dz/dy)(dy/ds)

=3lny.cost+6xsint/y.

Now substitute values of x and y in terms of s and t.

Hope this helps.Please RATE....

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