Math 208 (Lutz) - Quiz #2, 9/6/13
Name:
Directions: This quiz has 3 questions, for a total of 15 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. (5 points) A plane meets the z-axis at z = −4, has slope 3 in the y direction and slope −2 in the x
direction. What is the equation of the plane?
2. (5 points) Let g be the function of 3-variables given by
g(x, y, z) = x2 + y 2 + z 2 .
Give an equation for the level surface of g corresponding to c = 36 and sketch a graph of this level
surface.
3. (5 points) Let f (x, y) given by
f (x, y) =
x2 − y 2
.
x2 + y 2
Show that f does not have a limit as (x, y) → (0, 0).
Note: A complete solution to this problem must include a brief explanation of how your work
establishes that f does not have a limit as (x, y) → (0, 0).
[Hint: Use the lines y = 2x and y = 12 x.]