Math 2321 Spring 2009
Calculus III
First Midterm Exam
Friday, February 6
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. You must justify all of your answers to receive credit. Notatio
Math 2321 Spring 2009
Calculus III
Final Exam
Saturday, May 9
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. Except on multiple choice questions, you must justify all of your answers
Math 2321 Spring 2009
Calculus III
Third Midterm Exam
Monday, April 6
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. Except on multiple choice questions, you must justify all of your
Math 2321 Spring 2009
Calculus III
Second Midterm Exam
Wednesday, March 4
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. Except on multiple choice questions, you must justify all of y
Calculus III
Spring 2010
Exam 1
Practice Problems
Exercise 1. Consider the following four planes:
P1
P2
P3
P4
:
:
:
:
4x 2y + 2z = 4
5x + 2z = 5
x 4y + 3z = 1
6x + 3y 3z = 6
Which are parallel? Are any of them identical? For those pairs that are not paral
Calculus III
Spring 2010
Exam 3 Practice Problems
Problem 1. Evaluate the following integrals.
xy dA where R is the region bounded by the curves x = y 2 and y = x 2.
a.
R
1
1
b.
1
c.
y
2
yex
dx dy [Hint: Reverse the order of integration.]
x3
x dA where R
Calculus III
Spring 2010
Exam 2
Practice Problems
Exercise 1. Verify that the function z = ln(ex + ey ) satises the partial dierential equation
2z 2z
x2 y 2
2z
xy
2
= 0.
Exercise 2. Explain why the function f (x, y ) = x + e4y is dierentiable at the poi