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Math 10C.
Midterm Exam 2
February 27, 2008
Turn off and put away your cell phone.
You may one page of notes, but no calculators, books or other assistance.
Read each question carefully, and answer each question completely.
Show all of your work; no credit will be given for unsupported answers.
Write your solutions clearly and legibly; no credit will be given for illegible solutions.
If any question is not clear, ask for clarification.
#
Points
Score
1
10
2
10
3
10
4
10
Σ
40
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1. Let
f
(
x, y
) =
radicalbig
25
−
x
2
−
y
2
.
(a) (9 points) Write down the equations for the contours at heights 3, 4, and 5, and
draw a contour diagram with these three contours clearly labeled.
Solution: For
c
= 3, contour is the circle of radius 4 centered at the origin. For
c
= 4, contour is the circle of radius 3 centered at the origin. For
c
= 5, contour
consists of a single point (0
,
0).
(b) (1 points) Describe in words what the contours look like for height
c >
5.
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 Winter '07
 Hohnhold
 Math, Calculus, normal vectors

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