Multivariable Calculus Spring 2016
Test 1
Answer all questions carefully and completely. Put all work and your answers on the paper provided.
Partial credit may be awarded, so please show all of your
Calc C Review for final
Geometric entities in
R
3
:
Lines: All forms
Surfaces: Planes, spheres, cones, cylinders, oids, quadrics
Know intersections of these, level sets, traces, etc.
Vectors:
Lengths
Multivariable Calculus - Test 2
Fall 2016
Answer all questions carefully and completely. Put all work and your answers on the paper provided. Partial credit
may be awarded, so please show all of your
Multivariable Calculus - Test 2
Fall 2016
Answers
Part 1
2
f : R R be a continuous function and let
Let
R= [ a , b ] [c , d ] be a rectangle in the plane.
f ( x , y ) dA
A. What is the definition of
Multivariable Calculus - Test 2
Spring 2016
Answers
Part 1
Evaluate
xdA
where
D
between the
y -axis and the line
D is the region in the first quadrant inside the circle:
2
2
x + ( y 1 ) =1
y=x .
We d
Multivariable Calculus - Test 2
Spring 2017-Answers
Part 1
Let
f : R2 R be a function and let R= [ a , b ] [c , d ] be a rectangle in the plane.
a.
What is the definition of
f ( x , y ) dA
?
R
m
n
f
Multivariable Calculus Spring 2017
Test 1
Answer all questions carefully and completely. Put all work and your answers on the paper provided.
Partial credit may be awarded, so please show all of your
Multivariable Calculus - Test 1
Answers
Part 1
Let P=(6,9,7) , Q=(8,10,5) and R=(2,0,3) be points in R3 and let
w = 1,6,1 be a vector. Let l be the line containing P and Q .
a. Give the parametric for
Multivariable Calculus Spring 2016
Test 1-Answers
Part 1
A. Give the parametric equations of the line through the point
vector
v = 2,1,1 .
P=(5,1,2) in the direction of the
x=5+2 t
y=1t
z=2+t
B. Give
Review for test 2
Multivariable Calculus
Types of integrals:
f ( x , y ) dA
Double integrals:
D
To change into iterated integrals
Describe D :
Rectangular coordinates
Polar coordinates:
dA=dxdy
x=rco
Multivariable Calculus Fall 2015
Test 2-Answers
Part 1
Let f : R2 R
the plane.
be a continuous function and let
R= [ a , b ] [c , d ] be a rectangle in
A. What is the definition of
f ( x , y ) dA
?
R
Jack Hofmann
MAT 229
Dr. Clifford
March 28th,2017
# What was the key graphical observation from Technology Assignment 2?
Answer:
A key graphical observation I can make from Technology Assignment 2, is
Jack Hofmann
MAT 229
Dr. Clifford
March 28th, 2017
# 1. Change the input expression on the levelset module so that the corresponding level set is an
ellipse.
levelset[e_, k_] := Module[cfw_k1, set1, k
Ms. Carlton is planning a round-the-world trip as a retirement present to herself. She has estimated that
the cost, in dollars per day, of her trip is where x is the number of days she is on vacation.
Midterm Review
Find
dy
for each of the following:
dx
1. y = sin 4 (3 x 8)
2. y 2 = 4 x 3 y 2 2 x 2
3. y = ln(3 x 7)
4. y = ln 6 (2 5 x)
5. y = e6 x 11
6. y = 3xe3 x
7.x 3e 2 x 7 = 4 y 2
8. y = sec 2 3
2\
24,2008 MATH 211EXAM I -SePtember
lines l)Forthetwo intersecting x -2 : +(y + D : + k - 3)
andf(x-5):+(y-r):z-4
of the a)Determine coordinates the point wherethey intersect two lines these the b)De
MATH 211-EXAM III -November19' 2008 the l)Sketchthe regionof integration,reverse orderof integrationandevaluate
2 4-x2
J I #or*
0 0
and by 2)Evaluate convertingto polar coordinates integrating
rlr4
J
Math 211
Exam 1
September 27, 2006
Read each problem carefully. Please show all your work for each problem! Use only those methods discussed thus far in class. Always simplify when possible. No calcul
Math 213
Exam 2
October 25, 2006
Read each problem carefully. Please show all your work for each problem! Use only those methods discussed thus far in class. Always simplify when possible. No calculat
Math 211
Exam 3
November 29, 2006
Read each problem carefully. Please show all your work for each problem! Use only those methods discussed thus far in class. Always simplify when possible. No calcula
Math 211
Final Exam
December 20, 2006
Read each problem carefully. Please show all your work for each problem! Use only those methods discussed thus far in class. Always simplify when possible. No cal
Derivatives Test Review
Find
dy
for each of the following, circle answer:
dx
1. y = 3e3sin 2 x
2. y = ln(3 x 2 8)
3. y = ln 2 (2 x 5)
4. x 2 y 3 = e3 x
5. y = 3e 2 x + 4sin 5 x ln(2 x 5)
6. y = ln 7 3
1. y =
3 x( x 2) 2
Roots _ VA _ HA _
( x + 2)( x 4) 2
2. y =
2x
Roots _ VA _ HA _
( x 3) 2
3. y =
( x 2 9)( x 2 5 x + 6)
Roots _ VA _ HA_
x 2 ( x 2 16)
4. y =
x2
Roots _ VA _ HA _
x2 9
5. y =
2 x( x 3
Find the limit of each of the following:
1. lim(7 x 4) =
x 0
12. lim
x 0
2. lim
x 2
5x
=
2x 7
5
=
x 3 x + 3
3. lim
5x 8x 9
=
x
4x2 1
2
4. lim
9
=
x4
5. lim
+
x 4
6. lim
x 4
9
=
x4
9
=
7. lim
x 4 x 4
Limits Quiz Review Questions
Find the best, most descriptive answer to each of the following limit problems:
1. lim
x 2
5x 6
=
x + 3x + 2
2
10. lim
x 8
3x
=
x 2 7 x
2. lim
11. lim
5 x 5
=
x
12. lim
x
Limits Overview
When you are asked to evaluate a limit, you need to process your thoughts in an
organized fashion. The following lists the order you should be checking off in your
mind as you evaluate
THE COLLEGE OF NEW JERSEY
Department of Mathematics and Statistics
MAT 127 Section 2
Calculus A
Fall 2015
Instructor: Dr. S.Van der Sandt
Office: Science Complex P240
Phone: 609 771 3061
Email: vander