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Midterm

MATH 32A Study Guide - Midterm Guide: Level Set, Tangent Space, Directional DerivativeExam


Department
Mathematics
Course Code
MATH 32A
Professor
All
Study Guide
Midterm

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MATH 32A
PRACTICE FINAL EXAMINATION
Monday, June 6th 2016
Please show your work. You will receive little or no credit for a correct answer to a
problem which is not accompanied by sufficient explanations. If you have a question about
any particular problem, please raise your hand and one of the proctors will come and talk to
you. At the completion of the exam, please hand the exam booklet to your TA. If you have
any questions about the grading of the exam, please see the instructor within 15 calendar
days of the examination.
I certify that the work appearing on this exam is completely my own:
Signature:
Name: Section:
#1 #2 #3 #4 #5 #6
#7 #8 #9 #10 #11 Total
R
1

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2 32A PRACTICE FINAL RADKO
Problem 1. Suppose you are walking on the surface
z= 4x2+y22
directly above the curve
~r(t) = hcos t, sin ti, t [0,2π].
Find the values of tfor which you are walking uphill.

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32A PRACTICE FINAL Radko 3
Problem 2. Evaluate the following limit, or show that the limit does not exist.
lim
(x,y)0
xp|y|
x2+y.
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