Download Quiz 1

Math 208 (Lutz) - Quiz #1, 1/17/14
Name:
Directions: This quiz has 3 questions, for a total of 20 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. (5 points) Give an equation for a sphere of radius 8 centered at the point (2, 3, −1).
2. (7 points) Consider the function f given by f (x, y) = x3 − y + 1. On the same set of axes, draw graphs
of cross-sections of f with y fixed at y = 0, y = 1, and y = 2.
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3
2
1
-4
-3
-2
-1
-1
-2
-3
-4
1
2
3
4
3. (8 points) Sketch a contour diagram for the function f (x, y) = y + x2 with at least four labeled
contours.
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3
2
1
-3
-2
-1
1
-1
-2
-3
-4
2
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