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