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Homework 19
Sections 18.3 & 18.4
1. (6) Determine whether the vector eld
F~ (x, y, z) = (xye + 3)~i +
z
is path-independent.
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1
1 2 z
2
z
x e + 2z 1 ~j +
x ye + 2y ~k
2
2
2. (6) Use the Fundamental Theorem of Calculus for Line Integrals to compute

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Homework 11
Sections 14.6 & 14.7
z
z
and y
for z = u2e3w , u = xy2, w = ln(x3y).
1. (6) Find and simplify x
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2. (7) Find the quadratic Taylor polynomial, Q(x, y), approximating f (x, y) =
near (5, 6).
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p
(2x y)3
3. (7) Determine the best quadra

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Homework 13
Section 16.2
1. (2ea) Sketch the region of integration of the following.
Z
5
Z
x+1
(a)
2
x +y
0
2
Z
dy dx
4
Z
3
(b)
2
sin(xy) dx dy
0
y1
Z
2. (5) Evaluate the integral
and
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(3, 1).
2xy dA,
T
where
T
is the triangle with vertices
(1, 1)

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Homework 7
Sections 14.1 & 14.2
1. (2ea) The monthly payment on a home loan is a function, P (A, r, n), of the amount of
the loan, A, the interest rate, r, and the number of years of the loan, n.
positive or negative? Why?
(a) Is P
A
(b) Is Pn(A, r,

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1. (5) Find the equation of the plane which is tangent to the graph of
f (x, y) = yx3 xy 2 + xy + 11x
at the point (2, 4). Write your answer in the form z = ax + by + c.
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Homework 8
Section 14.3
2. (5) Find an equation for the tangent plane to the

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Homework 24
Section 20.1
1. (4) Compute the curl of
F~ = (5yz + x)~i + (3xz + y)~j + (9xy + z)~k .
= (2xy + z + 4)~i y 2~j + (11y 5x2 )~k and let C be the square of side
length 0.01 centered at (2, 3, 4) in the plane 2x + y + 2z = 14, oriented clockw

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Homework 20
Section 18.2
1. (5) Let C be the line segment from (1, 4, 9) to (5,Z 6, 8) and consider the vector eld
F~ (x, y, z) = (x + y)~i + (xz)~j + (y 4)2~k . Compute
F~ d~r.
C
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2. (3ea)
Consider the vector eld
F~ (x, y) = (x + y)2~i 5y~j
y
2
C

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Homework 6
Sections 13.3 & 13.4
1. (5) Consider the vectors ~q = 5~i ~j 4~k and m~ = 3~i + 2~j + ~k. Determine the component
of ~q that points in the same direction as m~ .
2. (5) Given the vectors ~v = 5~i + 2~j + 3~k and w~ = 3~i + ~j 4~k, compute

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Homework 3
Section 12.3
1. (3) Problem #16 on page 688 (section 12.3) of the text.
(a)
(b)
(c)
(d)
(e)
2. (5) Find an equation for the contour of f (x, y) = 5x2y xy3 + 44 that goes through the
point (3, 2).
3. (4) Determine which of the functions bel

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Homework 16
Section 16.5
which represent the volume inside the hemisphere bounded
1. (2ea) Set up triple integrals
p
by the graph of z = 12 x2 y 2 and the xy -plane in
(a) Cartesian coordinates
(b) Cylindrical coordinates
(c) Spherical coordinates
S1

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Homework 15
Section 16.4
1. (2,3) Sketch the region of integration for the following integrals.
(a)
Z
4
Z
2
(r + 1)r ddr
2
/4
(b)
Z
/4
3
sin rdrd
0
2. (4) Determine the integral of the function f (x, y) =
1 x2 + y 2 4.
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Z
1
cos
p
x2 + y 2 over th

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Homework 4
Section 12.5
1. (5) Describe the level surfaces of
f (x, y, z) =
e7z+x2 +y2 .
Be sure to include all important
information which may apply, such as orientation (up/down/left/right), vertex, radius,
etc.
2. (5) Describe (geometrically) the

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Homework 2
Section 12.4
(2, 1, 7),
1. (5) Determine an equation of the plane which passes through the points
5, 4,
35
, and
2
(2, 4, 13)
2. (3) Each of the following contour diagrams represent linear functions.
sponding plane, let
m
denote the slope

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Homework 9
Section 14.4
1. (3) Compute the gradient of
g(x, y) = sin (x + 2y) +
2. (4) Find the directional derivative of
the direction
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of ~
v = 4~i + 5~j .
y2
+3
x
at
, 2
f (x, y) = x2 ln y xy 2 + 2x
.
at the point
(3, 1)
in
3. (4ea) Consider th

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Homework 21
Sections 19.1 & 19.2
1. (2ea) Determine the ux of the vector eld F~ (x, y, z) = ~i + 2~j 3~k through the
rectangular regions with vertices listed below, assuming the orientation is the one
which is pointed away from the origin. [These are

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Homework 17
Sections 17.1 & 17.2
1. (15) Determine a parameterization for each of the following.
(a) The line through the points (4, 2, 1) and (1, 7, 5).
(b) The circle of radius 9, parallel to the xz-plane, centered at (5, 4, 3).
(c) The line segmen

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Homework 10
Sections 14.4 & 14.5
1. (5) Consider the function f (x, y). If you start at the point (4, 6) and move toward the
point (7, 2), the directional derivative is 2. If you start at the point (4, 6) and move
toward the point (8, 9), the directi

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Homework 22
Sections 19.2
1. (6) Let S be the portion of the graph of z = 8x3 +y 2 +y which lies above the triangle
in the xy -plane with vertices (0, 1), (2, 5), and (0, 5). Find the ux of the vector eld
F~ (x, y, z) = (y 32 xy)~i (y 2 + 8 z)~j + (2

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Homework 14
Section 16.3
1. (3ea) Consider a material of varying density whose whose density is given by
2
xy+z +1.
(x, y, z) =
Set up triple integrals, in Cartesian coordinates, including limits of integration
which represent the mass of the solids