DETAILED ANSWERS TO PROBLEM 9:
1. The correct answer is (b).
(a) is FALSE. If F is incompressible (i.e. div F = 0) then F = curl A for some vector eld A,
but F is not necessarily conservative. For example, F = y, x, 0 is incompressible (div F = 0)
but cur

Mathematics 32B - Practice Final Examination
Instructor : D. E. Weisbart
NAME (please print legibly):
Your University ID Number:
Your Discussion Section and TA:
Signature:
There are ten questions on this examination.
Calculators, notes and books may not

Right Skewed More values on the left. Mean larger than median.
Standard deviation s = (x-xx)2/n-1
Variance = s2
Z = x xx / s
IQR = Q3 Q1;
range = max - min
correlation coefficient r = zxzy / n-1
Predicted y = a + bx
b = r (sy /sx)
a = ybar bxx
P(A and B)

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1. (15 pts) Consider a model of the population of Moose (M) and Wolves
(W) on Isle Royale, based on the following assumptions:
7 0 Without the wolves around, the Moose population grows logistically,
M i with a growth rate of 0.3 per yea

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Math 33A Midterm 1 Study Guide
Instructor: David Wihr Taylor Fall 2007
1
Overview
The rst midterm exam will cover all the material in the lectures (with the exception of change of coordinates), which corresponds to the material in sections 1.2-3.3 of the

Math 33A Midterm 2 Study Guide
Instructor: David Wihr Taylor
Fall 2007
1
Overview
The second midterm exam will cover all the material in the lectures (including the material from the rst
midterm because the course is cumulative). However, it will emphasiz

Math 33A Final Review
Instructor: David Wihr Taylor
Fall 2007
1
Overview
The nal exam is cumulative and will cover all the material in the lectures. Your review should, therefore,
include the information on the study guides for each of the rst two midterm

MATH 32B
FIRST MIDTERM EXAMINATION
October, 22nd, 2007
Please show your work. You will receive little or no credit for a correct answer to a
problem which is not accompanied by sucient explanations. If you have a question about
any particular problem, ple

Mathematics 32B - Practice Midterm 1
Instructor : D. E. Weisbart
NAME (please print legibly):
Your University ID Number:
Your Discussion Section and TA:
Signature:
There are FOUR questions on this examination.
Calculators, notes and books may not be use

Part 1: Short Answer Problems (Worth 48%)
For full credit you need to show all your work. .
1. [12%] Refer to the ﬁgure below. The vertical distance between points A and B
represents a tax in the market.
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a. Find the Ber-unitﬂrden of