- 1.
- Find the integral of the function f(x,y) = x over the region R lying between the graphs of the curves

- 2.
- Find the integral of the function f(x,y,z) = z over the region S bounded by the planes

- 4.
- Find the critical points of the function

- Describe what the Second Derivative Test says about each critical point.

**5.** (15 pts.) Calculate the first and second partial derivatives of the function

**1.** (25 pts.) Find the critical points of the function

and determine which of *rel max*, *rel min*, or *saddle point*, each is.

**2.** (20 pts.) Find the maximum value of the function

subject to the constraint g(x,y) = x^{2}+2y^{2} = 5 .

**5.** Evaluate the following double integrals (10 pts. each):

(a): ò_{0}^{1} ò_{1}^{2} x^{2}y-y^{2}x dx dy

(b): ò_{0}^{1} ò_{Öx}^{1} xÖy dy dx

**5.** (20 pts.) Evaluate the integral

by changing the order of integration.
(Trust me, you **can't** evaluate
it in the order in which it is given!)

**2.** (20 pts.) Find the local extrema of the function

and determine, for each, if it is a
local max. local min, or saddle point.

**3.** (20 pts.) Find the maximum and minimum values of the
function

subject to the constraint

**4.** (20 pts.) Evaluate the interated integral

by rewriting the integral to reverse
the order of integration.

(Note: the integral *cannot* be evaluated in the order given....)

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