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1. (20 pts.) Find the equation of the plane in 3-space which passes though the three points

Does the point (1,2,9) lie on this plane??

2. (20 pts.) Find the partial derivatives of the following functions:

(a) f(x,y,z) = x²y⁷-3yz³+cos(x-y)

(b) g(x,y) = [(xy-3y+2)/((x+y)²-y³)]

3. (20 pts.) Find the equation of the tangent plane to the graph of the function

at the point (2,1,11) .

4. (20 pts.) Sketch the level curves of the function

for z-values 0, 1, 2, and -1 . (Hint: solve for y ....) Be sure to label everything appropriately.

5. Find the derivatives of the function

at the point (1,0,-1), in the directions of the vectors

In what direction is the function f decreasing the fastest, at the point (1,0,-1) ??

6. (20 pts.) If

where

use the Chain rule to find [df/dt] when t = 1 .