Midterm Exam 2 Solutions
Math 32B/1, Spring 2013
3
cos t3 , sin t3 , t2
2
1. Let C be the space curve with parametrization c(t) =
May 13
, for 0 t 3.
Find the length of C .
Solution:
C
ds =
3
0
2
The length of C is
3
|c (t)| dt, so we compute
c (t) = 3t s

Final Exam Solutions
Math 32B/1, Spring 2013
June 11
1. Consider the boxes E1 = [3, 3] [3, 3] [1, 1] and E2 = [2, 2] [2, 2] [1, 1] in (x, y, z )space. Let E = E1 \ E2 be the region consisting of those points in E1 that are not in E2 , shown
below, and giv

Math32B Discussion Section Notes
Jiayin Guo
April 18, 2014
It is a growing note for Math32B. It is designed to be a supplement of what I said in
the discuss session. Thus all the answer will be provided but only some problems will be
given detailed soluti

Math 32B
Practice Final
1. Write down Greenes theorem including all hypothesis and its conclusion. Write down
the denitions of any terms which appear in the theorem.
Solution: See page 1009 in your textbook. Important terms to know are boundary
orientatio

MATH 32B, Section 3 - Practice Midterm One
Name:
Student ID Number:
Instructions:
This is a practice exam for the first midterm examination in MATH 32B. You should
follow the following rules when preparing with this midterm:
1. This exam is meant to be 50

Math 32A Practice Midterm 1
February 5th, 2014
Your name:
Your SID:
There are four problems on this exam, each worth ten points. You have
fifty minutes. Good luck!
1
Problem 1: Consider vectors v = h12, 3, 4i and u = h1, 2, 2i. Find
the projection of u on

Statistics 10
Introduction to Statistical Reasoning
Fall 2013
Instructor: Nathan Langholz
Room and time: MWF 9:00 - 9:50A BUNCHE 1209B
Office: 9432 Boelter Hall
Office Hours: Monday and Wednesday 2:30 to 4:00 or by appointment
Email: langholz@stat.ucla.ed

Final Exam Sample
Math 32B/2, Spring 2014
This is a collection of problems that would not be unreasonable for a real final exam.
WARNING: the inclusion (or exclusion) of a certain topic or type of problem on this sample
exam does not guarantee its inclusi

MATH 31B LECTURE 1 AND 3
PRACTICE MIDTERM
1
2
MATH 31B LECTURE 1 AND 3 PRACTICE MIDTERM
Problem 1. (Multiple choice, 10 pts) Evaluate the improper integral
Z 1
1
dx
1 x
Indicate your answer in the box below:
(a) 1; (b) 0; (c) 1; (d) integral diverges; (e)

Midterm Exam 2 Sample
Math 32B/2, Spring 2014
This is a collection of problems that would not be unreasonable for a real midterm exam.
WARNING: the inclusion (or exclusion) of a certain topic or type of problem on this sample
exam does not guarantee its i

Midterm Exam 1 Sample
Math 32B/2, Spring 2014
This is a collection of problems that would not be unreasonable for a real midterm exam.
WARNING: the inclusion (or exclusion) of a certain topic or type of problem on this sample
exam does not guarantee its i

M IDTERM 1
April 24, 2002
Instructions.
Please show your work. You will receive little or no credit for an answer
not accompanied by appropriate explanations, even if the answer is correct.
If you have a question about a particular problem, please raise y

Math 32B, Lecture 4
Multivariable Calculus
Sample Final Exam
Instructions: You have three hours to complete the exam. There are ten problems, worth a
total of one hundred points. You may not use any books, notes, or calculators. Show all your
Work; partia

Math 32B, Lecture 4
Multivariable Calculus
Sample Final Exam
Instructions: You have three hours to complete the exam. There are ten problems, worth a
total of one hundred points. You may not use any books, notes, or calculators. Show all your
work; partia