1
Math 2057 - Exam 3 - Key
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes, or
calculator. READ THE DIRECTIONS FOR EACH PROBLEM CAREFULLY. Once you get y
1
Math 2057
Quiz 8 Key
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes,
calculator, or fellow classmates. Problem on back!
1. Find the Jacobian of the tr
1
Math 2057
Quiz 4 - Key
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes,
calculator, or fellow classmates.
1. Use the Method of Lagrange Multipliers to
1
Math 2057
Quiz 1
Name: Key
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes,
calculator, or fellow classmates.
1. Create a contour plot by sketching the
1
Math 2057 - Exam 1 Key
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes, or
calculator.
1. (16 points) Is
(
f (x, y) =
xy
2x2 +y 2
if (x, y) 6= (0, 0)
0
1
Math 2057 - Exam 2
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes, or
calculator. READ THE DIRECTIONS FOR EACH PROBLEM CAREFULLY. Once you get your an
1
Math 2057
Quiz 6 - Key
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes,
calculator, or fellow classmates.
1. Evaluate.
ZZ
2 sin(x2 + y 2 ) dA,
R
R is t
1
Math 2057
Quiz 2 Key - Due Monday, 9/12/16
Instructions: Answer the following questions on a separate sheet of paper. You must show ALL necessary
work to get credit. You may work together. HOWEVER,
1
Math 2057
Quiz 3 - Key
Instructions: Answer the following questions on a separate sheet of paper. You must show ALL necessary
work to get credit. You may work together. HOWEVER, THE WORK YOU TURN IN
1
Math 2057
Quiz 5 - Key
Instructions: You must show ALL necessary work to get credit. You may not use your book, notes,
calculator, or fellow classmates.
1. Evaluate the partial integral.
Z 2
y + xey
3.7 Optimization
Monday, January 4, 2016
7:20 AM
Procedure:
1. Understand the problem
a. What is the unknown? What are the given quantities?
2. Draw a diagram
3. Notation: Assign a symbol to the quan
Math 1552(1-4) Spring 2011 Final Exam
Answer any 10 questions.
1. Use integration by parts to evaluate the following integrals
(a)
!
x cos 5xdx
!
(b)
(2x + 1)e3x dx.
2. (a) Use a suitable trigonometri
Math 1552 (11-15) Final Exam Fall 2012
Answer any 10 questions. In order to earn partial credit, please show all of your
work.
1. (a) Use integration by parts to evaluate the integral
!
(b) Evaluate t
Math 1552(5-8) Final Exam Fall 2011
Answer any 10 questions. In order to earn partial credit, please show all of your
work.
1. (a) Use integration by parts to evaluate the integral
!
xe2x dx
!
cos3 x
2MATH 1550,
REVIEW for FINAL
1. Evaluate each limit. You may use LHospitals rule where applicable. If the limit does
not exist, justify your answer.
(a)
sin x x
x 0
x3
lim
(b)
lim x ln x
x 0
2 Find a
Calculus Cheat Sheet
Limits
Definitions
Precise Definition : We say lim f ( x ) = L if
Limit at Infinity : We say lim f ( x ) = L if we
x a
x
for every > 0 there is a > 0 such that
whenever 0 < x a <
Calculus Final
December 10, 2014
7:30 AM
Anything questions on test reviews/tests are fair game to study
Chapter Two
I.
Limits
Limits to infinity
One-sided limits
Infinite limits (vertical asymptot
Related Rate-Word Problems
. Draw a diagram and label the quantities that don’t change with their respective values and quantities
that do change with respect to time as variables.
2. Mathematically s