Math 2210
Practice Midterm #2
Instructor: Mike Shrieve
Name:
The midterm is 50 minutes. No calculators or equation sheets are allowed. Answer all
questions.
1
(1) Let f = (x2 + y 2 − 9) 2 . Sketch√the domain of f . Sketch and label the level curves of
f (x, y) = k for k = 0, 4, and 2 10.
(2) In what direction is the function f (x, y) = 9x4 + 4y 2 increasing most rapidly at the
point (1, 2)?
(3) Let f (x, y) = ln( xy ) and let x = u2 + v 2 + w2 and y = uv. Find fu , fv , and fw .
(4) Find the extrema of f (x, y) = x2 y − 6y 2 − 3x2 .
(5) Find the extrema
of f (x, y) = x2 y subject to the constraint x2 + y 2 = 4.
R 1 R √x
(6) Evaluate 0 x xy dy dx.
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