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