Math 208 (Lutz) - Quiz #1, 8/30/13
Name:
Directions: This quiz has 4 question, for a total of 20 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. (6 points) Consider the points A = (34, 72, 10), B = (−23, 60, 15) and C = (−35, 72, 20).
1. Which point is closest to the xy-plane? Justify your answer.
2. Which point is farthest from the yz-plane? Justify your answer.
3. Which point is closest to the xz-plane? Justify your answer.
2. (6 points) Find the equation of a circle of radius 5 centered at (1, −2, 3).
3. (6 points) Consider the function f given by f (x, y) = y 3 + x. Draw graphs of cross-sections with x
fixed at x = −1, x = 0, and x = 1.
4
3
2
1
-4
-3
-2
-1
1
2
3
4
-1
-2
-3
-4
4. (4 points) Find an equation of the contour of g(x, y) = 3x2 y + 7x + 20 that goes through the point
(5, 10).