Math 227-104 (CRN 24680)
Carter
Study Guide
Spring 2015
General Instructions.
1. Find equations of the tangent plane and normal line to the w = 0 level
surface of f (x, y, z), at a specific point.
2. For a function f (x, y),
(a) Find ∇f
(b) Find the directional derivative of f at a point P0 , in a specific direction v — observe that you’ll need to normalize v.
(c) Find the maximum rate of change of f at the point P0 , and state
the direction in which it occurs.
3. (a) Find and classify the critical points of some function f (x, y).
(b) Use Lagrange multipliers to find the maximum and minimum values
of some function f (x, y), subject to some constraint g(x, y) = 0.
4. Evaluate the integral
Z
~b
M dx + N dy + P dz.
~a
5. Use Green’s Theorem to evaluate
I
M dx + N dy
C
where C is the boundary of some standard object.
6. A question about the area form.
7. Study Example 5 page 907.
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