Math-2415 Multivariable Calculus
Homework 6
Turn it in to the TA who is in charge of your Problem Session during the week of October 14, 2013
Name:
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class
NAME: SOLU "Tlon-
4 /85 m m /75
MATH 251H (Fall 2006) Exam 2, Oct 27th
No calculators, books or notes!
Show all work and give complete explanations for all your answers.
This is a 75 minute exam. It is worth a total of 75 points.
(1) [15 pts] Either com
NAME:
1
/12 2
/10 3
/5
4
/10 5
/10 6
/8
7
/10 8
/10 9
/5
10
/8
/8
/4
11
12
T
/100
MATH 2415 (Spring 2014, ZWECK) Final Exam
No calculators, books or notes! Show all work and give complete explanations. This 2 hours 30 mins
exam is worth 100 points.
(1) [1
NAME; |
1 /12 2 /18 3 /17 4 /18 5 /10 T /75
MATH 251H (Fall 2006) Exam 11 Sept 27th
No calculators, books or notes!
Show all work and give complete explanations for all yoar answers.
This is a 75 minute exam. It is worth a total of 75 points.
/
b
(1
Dr. Zwecks Class
No calculators, books or notes! Show all work and give complete explanations. Dont spend too much
time on any one problem. This 75 minute exam is worth 75 points.
_) A
(1) [12pm] r 0/
(a) Find a vector parametrization of the line through
1 f m /126
MATH 2415 (Fall 2014;) Exam I, Oct 3rd
No books or notes! You may use a scientic calculator provided it does not allow for access
Show all workand give complete explanations. Dont spend too much time on any one
75 minute exam is worth 75 poin
NAME: SOLUWO MS
3 ml; /1o| 5 ml 6 /14 T /75l j
MATH 251H (Fall 2006) Exam 3, Nov 22nd
1 no
2 /12
No calculators, books or notes!
Show all work and give complete explanations for all your answers.
This is a 75 minute exam. It is worth a total of 75
NAME: SOL O ALS
- 4 /12
)
MATH 251 (Fall 2010 Exam II, Oct 21st
No calculators, books or notes! Show all work and give complete explanations. This 65 min exam is
worth 50 points.
(1) [6 pts] Suppose that
x=3u+2v, y=4u51}
and let 2 : f (ac, y) be a functio
MATH 251 (Spring 2004) Exam 2, March 3181;
No calculators, books or notes!
Show all work and give complete explanations for all your answers.
This is a 65 minute exam. It is worth a total of 75 points.
(1) [8 pts] Does the limit exist? Explain why, and if
NAME: gOLUWQd-S
4 714
)
MATH 251 (Fall 2010 Exam I, Sept 23rd
No calculators, books or notes! Show all work and give complete explanations. This 65 min exam is
worth 50 points.
(1) [10 pts] Let u = (6, O, 8) and v = (1, 2, 3) be two vectors in space.
(a)
Differentiation Rules
d
Product Rule: 5 [f(x)g(x)] = f (x) g(x) + f '(x)g(x)
a _
Power Rule: Ex" = nx" 1
Quotient Rule: 1 -g(x)fl(x) f(x)g'(x)
dx 9(x) L900]2
d d d
Chain Rule: a[f(g(x)] = f(g(x) - g(x) = a; if y = u) and u = g(x)
Useful Derivatives Useful
Sample Exam 1
Math 2415 Calculus of Several Variables
1. Find the line through (3; 1;
2) that intersects and is perpendicular to the line
8
1+t
< x =
y =
2+t :
l:
:
z = 1+t
2. Find the equation of the plane containing the points (3;
cross-products suitabl
Sample Final Exam
Math 2415 Calculus of Several Variables
1. Find the following line integrals
R
a) C !; where ! = yz dx + xz dy + xy dz; and C consists of straight-line segments joining (1; 0; 0) to
(0; 1; 0) to (0; 0; 1)
R
b) C !; where ! = x2 dx xy dy+
Math-2415 Multivariable Calculus
Homework 8
Turn it in to the TA who is in charge of your Problem Session during the week of October 28, 2013
Name:
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class
Review Problems for II Midterm Exam
Math 2415 Calculus of Several Variables
1. Consider the function F : R2 R3 ,
F (x, y) = (x3 y, 2x + y, y + x4 )
and G : R3 R2 is
G(u, v, w) = (2u + 3v w, 2uvw).
Answer the following questions:
i) Find F G;
ii) Use the c
Math-2415 Multivariable Calculus
Quiz 11
December 9, 2013
Due on Friday, December 13
Name:
Instructions. Please solve the following problems (show all your work ). Please let me know if you have
any questions concerning the problems.
1. (10 pts) Find the
Review Problems for II Midterm Exam
Math 2415 Calculus of Several Variables
1. Consider the function F : R2 ! R3 ,
F (x; y) = (x3 y; 2x + y; y + x4 )
and G : R3 ! R2 is
G(u; v; w) = (2u + 3v
w; 2uvw):
Answer the following questions:
i) Find F
G;
ii) Use t
Math-2415 Multivariable Calculus
Homework 11
Turn it in to the TA who is in charge of your Problem Session during the week of December 1, 2013
Name:
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class
Review Problems for II Midterm Exam
Math 2415 Calculus of Several Variables
Solutions
by Dr:V:Ramakrishna & Dr:M:Dabkowski
1. Consider the function F : R2 ! R3 ,
F (x; y) = (x3 y; 2x + y; y + x4 )
and G : R3 ! R2 is
G(u; v; w) = (2u + 3v
w; 2uvw):
Answer
Math-2415 Multivariable Calculus
Homework 3
Turn it in to the TA who is in charge of your Problem Session during the week of September 23, 2013
Name:
Instructions. Please solve the following problems (show all your work ). You can use your textbooks, clas
Solutions Review Problem for Math 2415
Calculus of Several Variables
1. Solve the following problems:
a) Find two nonparallel vectors, both orthogonal to (1; 2; 3).
b) Find the only v 2 R3 such that
(
v (i j) = k
v (i j) = 3
c) Find the line through (1; 1
MTH 254
CHAPTER 9
9.1
6. (a) In R2, the equation x = 4 represents a line parallel to
the y-axis. In R3, the equation x = 4 represents the
set cfw_(x, y, z) | x = 4, the set of all points whose
x-coordinate is 4. This is the vertical plane that is
parallel
MATH 2004 Homework Solution
Han-Bom Moon
Homework 1 Model Solution
Section 12.1 12.4.
12.1.11. Find an equation of the sphere with center (3, 2, 5) and radius 4. What is the
intersection of this sphere with the yz-plane?
Equation of the sphere:
(x (3)2 +
Math 2415
Homework on 12.6
1. Use traces (slices) to sketch and identify the surfaces in R3 given by the following
equations.
(a) 4x2 + y 2 = 16
(b)
x
4
=
2
y2
+ z9
4
2
(c) x2 + y 2x = 0 (Hint: Complete the square in x.)
(d) y 2 = x2 + z 2
(e) x2 + y 2 +
Vectors
Subtracting and Adding Vectors
Aim
To show how to subtract and add vectors.
Learning Outcomes
At the end of this section you will be able to:
Subtract/add one vector from/to another,
Subtract and add vectors written in component form,
Understan
MATH 264 R E V I E W
TOPICS COVERED
EXAM
1
(Chapters 12,13,14.1)
1. Vectors
add, subtract, multiply vectors, also graphically
magnitude of vectors
find relation between vectors
find resultant force if several forces are applied
2. Dot Product and Cross Pr