Version 030 EXAM 1 he (53090)
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001
10.0 points
Let f be a continuous function on [3, 1]
such that
f (3) = 1 ,
f (1
Math 408M
Week 5 Lecture 1 Activity
1. Consider r.t / D cos.t /; sin.t /; t ln.t / .
a) Does lim r.t / exist?
t !0C
b) Describe and sketch the graph of r.t /.
2. Describe and sketch the graphs of the following functions.
a) r.t / D sin.t /; t; cos.t /
b)
Math 408M
Week 4 Lecture 3 Activity
June 27, 2014
1. Find vector, parametric, and symmetric equations for the following lines.
a) the line through the point .1; 0; 3/ parallel to h2; 4; 5i
b) the line through the point .1; 0; 6/ perpendicular to the plane
Math 408M
Week 5 Lecture 2 Activity
July 2, 2014
1. Consider a particle A whose position at time t is given by sin.3t /; cos.3t /; 4t and a particle B whose position at
time t is given by sin.4t /; cos.4t /; 3t .
a) Find the speed functions for each parti
Math 408M
Week 5 Discussion 2 Activity
July 3, 2014
This is a review for the rst exam. Please note that it is not a promise of exactly what will or will not be on the exam.
Covering everything would require a very large number of problems. This is a revie
Math 408M
Week 6 Discussion 1 Activity
1. Suppose that the position of a particle at time t is given by r.t / D e t ; e t ; 2t .
a) Make an educated guess about when this particle is traveling the slowest.
b) Test your guess by determining when this parti
Math 408M
Week 6 Lecture 2 Activity
1. Determine and sketch the domains of the following functions.
a) f .x; y/ D ln.x y C 4/
p
b) f .x; y/ D x y 2
c) f .x; y/ D 1=x
d) f .x; y/ D 1=xy
2. Describe and sketch the graphs of the following functions.
a) f .x;
Math 408M
Week 6 Discussion 2 Activity
Describe and sketch the graphs of the following functions.
1. f .x; y/ D e xy
2. f .x; y/ D sin.x C y/
3. f .x; y/ D sin.x 2 C y 2 /
4. f .x; y/ D sin jxj C jyj
5. f .x; y/ D sin.xy/
6. f .x; y/ D sin jxyj
July 10, 2
Math 408M
Week 7 Discussion 1 Activity
July 15, 2014
1. Describe the graph of
f .x; y/ D
sin.x 2 C y 2 /
;
x2 C y2
including its limit behavior at the origin. Can this function be made continuous by dening a value for f .0; 0/?
2. Suppose that f .x; y/ ha
Math 408M
Week 7 Lecture 2 Activity
1. Find the partial derivatives of the following functions.
a) f .x; y/ D xy
y2
b) f .x; y/ D sin.x
y/
c) f .x; y/ D ln.x 2 C y 2 C 1/
d) f .x; y/ D 2xy sec.x/
2. Let f .x; y/ D xye y . Show that fxy .x; y/ D fyx .x; y/
Math 408M
Week 7 Lecture 1 Activity
July 14, 2014
1. Evaluate the following limits.
a)
b)
c)
x2
.x;y/!.0;0/ x 2 C y 2
lim
lim
.x;y/!.0;0/ x 2
x2 C 1
C y2 C 1
x2 y2
.x;y/!.0;0/ x 2 C y 2
lim
2. Describe the graph of
f .x; y/ D
sin.x 2 C y 2 /
;
x2 C y2
inc
Math 408M
Week 5 Discussion 1 Activity
July 1, 2014
1. Find a vector function that represents the intersection of the surfaces x 2 C y 2 D 4 and D xy.
2. Consider r.t / D t 2 ; 1
t;
p
t .
a) Find the tangent vector at t D 3.
b) Find an equation for the l
Math 408M
Week 4 Lecture 2 Activity
1. Find the cross products a
June 25, 2014
b of the following pairs of vectors.
a) a D h1; 2; 3i, b D h4; 5; 6i
b) a D h1; 2; 3i, b D h4; 8; 12i
c) a D h1; 2; 3i, b D h1; 2; 3i
2. Consider the following vectors.
jbj D 1
Math 408M
Week 4 Discussion 1 Activity
June 24, 2014
1. Work is dened as the product of the distance moved and force. If the force acts in the direction of the movement,
then computing work is simple. If it is not in that direction, then we must compute t
pennington (elp692) Homework 12.3 karakurt (56280)
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001
10.0 points
Determine the dot product of the vectors
a = 3
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bachmann-padilla (tnb574) Homework 1 maggi (53000)
mlmlmlmlmlmllmlmlnknk
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before answering.
001
1.0 points
1
1.
klmlmlmlmlmlmlmlmlmlml
bachmann-padilla (tnb574) Homework 3 maggi (53000)
mlmlmlmlmlmllmlmlnknk
This print-out should have 10 questions.
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before answering.
001
1.0 points
Find
klmlmlmlmlmlmlmlmlmlml
bachmann-padilla (tnb574) Homework 4 maggi (53000)
mlmlmlmlmlmllmlmlnknk
This print-out should have 15 questions.
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001
1
2. not isocel
klmlmlmlmlmlmlmlmlmlml
bachmann-padilla (tnb574) Homework 5 maggi (53000)
mlmlmlmlmlmllmlmlnknk
This print-out should have 15 questions.
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001
0.7 points
1
to
klmlmlmlmlmlmlmlmlmlml
bachmann-padilla (tnb574) Homework 6 maggi (53000)
mlmlmlmlmlmllmlmlnknk
This print-out should have 10 questions.
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001
1.0 points
r(s)
klmlmlmlmlmlmlmlmlmlml
bachmann-padilla (tnb574) Homework 7 maggi (53000)
mlmlmlmlmlmllmlmlnknk
This print-out should have 20 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
1
1
(x, y) : x2
klmlmlmlmlmlmlmlmlmlml
bachmann-padilla (tnb574)
mlmlmlmlmlmllmlmlnknk Homework 2 maggi (53000)
This print-out should have 10 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
1.0 points
002
Math 408M
Week 4 Lecture 1 Activity
June 23, 2014
1. Compute the dot products of the following pairs of vectors.
a) h3; 2i and h7; 4i
b) i C 4j
2k and 3i
j C 6k
c) h3; 2; 1i and h1; 2; 1i
2. Use the dot product to compute the angles between the following
Math 408M
Week 4 Discussion 2 Activity
June 26, 2014
1. Consider the following vectors.
a
b
Determine the signs of each component of a
b and of b
2. Give an example of three vectors in R3 such that a
.b
a.
c/ .a
b/
c.
3. Consider the quadrilateral Q with
Math 408M
Week 7 Discussion 2 Activity
1. Consider the function
(
x2
f .x; y/ D
0
xy
C y2
July 17, 2014
if .x; y/ .0; 0/
if .x; y/ D .0; 0/
a) Prove that f .x; y/ is not continuous at .0; 0/.
b) Prove that fx .0; 0/ and fy .0; 0/ both exist.
2. Prove that
Math 408M
Week 8 Lecture 1 Activity
July 21, 2014
1. Find d=dt in each of the following cases.
a) D x ln.x C 2y/, x D sin.t /, y D cos.t /
b) D ye x=y , x D t 2 , y D 1
t
c) D sin.xy/, x D 2t , y D t 5
2. Find @=@s and @=@t in each of the following cases.
Math 408M
Week 7 Lecture 3 Activity
July 18, 2014
1. Find equations for the tangent planes of the following surfaces at the given points.
a) D y 2
x 2 , . 4; 5; 9/
b) D sin.x C y/, .1; 1; 0/
c) D sin.x C y/, . =4; =4; 1/
d) D e x ln.y/, .3; 1; 0/
2. Find
Math 408M
Week 11 Lecture 2 Activity
August 13, 2014
1. Find the Jacobians of the following transformations.
a) x D u2
b) x D
v 2 , y D u2 C v 2
v
u
,y D
uCv
u v
2. Evaluate the following integrals using the given transformations.
a)
3x C 4y dA, where R i
Math 408M
Week 11 Discussion 2 Activity
1. Evaluate the following integrals.
a)
xy dA, where R is the region bounded by 2x
y D 1, 2x
yD
August 14, 2014
3, 3x C y D 1, and 3x C y D
R
b)
y x
dA, where R is the polygon with vertices at .1; 0/, .2; 0/, .0; 2/
Math 408M
Week 2 Lecture 1 Activity
June 9, 2014
1. Below are six parametric functions and their graphs. Match the functions with the graphs.
a) x D t 3
1, y D 2
t2
b) x D t C sin.2t /, y D t C sin.3t /
c) x D t 3
2t, y D t 2
t
d) x D cos.t /, y D sin t C