morrell (mm59638) HW 12.1 radin (56025)
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001
10.0 points
1
5. length = 6
6. length = 41 correct
Explanation:
We have
CALCULUS III
Paul Dawkins
Calculus III
Table of Contents
Preface . iii
Outline . iv
Three Dimensional Space. 1
Introduction . 1
The 3-D Coordinate System . 3
Equations of Lines . 9
Equations of Planes .
morrell (mm59638) HW 10.4 radin (56025)
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001
1
i.e. at = /2. Thus the area of the shaded
region is given by
I =
10.0
morrell (mm59638) HW 10.1 radin (56025)
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001
1
Consequently,
P =
2C,
C2
3
=
12 12
,
5 25
.
10.0 points
keywords: par
morrell (mm59638) HW 10.3 radin (56025)
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001
C. TRUE:
4 cos(4/3) = 2 , 4 sin(4/3) = 2 3 .
002
10.0 points
Which, if
morrell (mm59638) HW 13.2 radin (56025)
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001
10.0 points
Which of the following equations hold for all
dierentiable v
morrell (mm59638) HW 13.1 radin (56025)
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001
1
Find the domain of the vector function
r(t) = t2 , t 1, ln(4 t) .
1.
morrell (mm59638) HW 14.2 radin (56025)
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001
Suppose that
10.0 points
lim
(x,y)(2,3)
f (x, y) = 7.
What is the value
morrell (mm59638) HW 14.3 radin (56025)
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001
10.0 points
From the contour map of f shown below
decide whether fx , f
morrell (mm59638) HW 14.1 radin (56025)
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001
Find the domain of the function
1
1
(x, y) : x2 + y 2 > 1
4
5
1
1
(x, y)
morrell (mm59638) HW 14.5 radin (56025)
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001 10.0 points
dz
Determine
when
dt
1
002
10.0 points
z
Use the Chain Rule
morrell (mm59638) HW 14.4 radin (56025)
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001
10.0 points
keywords: linearization, partial derivative,
radical functio
morrell (mm59638) HW 14.7 radin (56025)
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001
10.0 points
Suppose (1, 1) is a critical point of a function f having c
morrell (mm59638) HW 14.6 radin (56025)
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001
1
2.
10.0 points
When z = P (x, y) is the pressure at a point
(x, y) in
morrell (mm59638) HW 15.1, 15.2 radin (56025)
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001
1
The graph of the function
z = f (x, y) = 7 x
is the plane shown
morrell (mm59638) HW 14.8 radin (56025)
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001
10.0 points
Use the method of Lagrange multipliers to
minimize
f (x, y)
morrell (mm59638) HW 15.4 radin (56025)
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001
(3 + 2 tan1
D
tan1
dxdy
(3 + 2) rddr
0
4
3 + 2
=
0
when D is the region
morrell (mm59638) HW 15.3 radin (56025)
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001
Consequently,
I =
10.0 points
002
Find the value of the double integral
Version 024 FINAL EXAM radin (56025)
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001
4.0 points
with respect to x with y xed we use the
substitution u = x2 + 5
Multivariable Calculus Study Guide:
A
A L TEX Version
Tyler Silber
University of Connecticut
December 11, 2011
1
Disclaimer
It is not guaranteed that I have every single bit of necessary information for
the course. This happened to be some of what I neede
morrell (mm59638) HW 4.4 radin (56025)
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001
x0
10.0 points
Determine if the limit
lim
10.0 points
x0
2cos(x) 2
3 x2
morrell (mm59638) HW 11.1 radin (56025)
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001
10.0 points
If
lim an = 2,
n
1
3. the sequence diverges
5
4
5
5. limit
morrell (mm59638) HW 11.2 radin (56025)
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001
10.0 points
If the nth partial sum of an innite series is
Sn =
n2 2
,
5
morrell (mm59638) HW 11.3 radin (56025)
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001
1
the solid blue line is the graph of f on [4, )
and the areas of the r
morrell (mm59638) HW 11.5 radin (56025)
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001
is divergent because
lim (1)
1.
n=1
2.
n=1
This leaves only the series
1
morrell (mm59638) HW 11.6 radin (56025)
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001
hence convergent. Consequently, the given
series is
absolutely converge
morrell (mm59638) HW 11.4 radin (56025)
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001
10.0 points
By the Divergence Test, therefore, series (A)
diverges .
(B
morrell (mm59638) HW 11.8 radin (56025)
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001
1
We have still to check for convergence at
x = 1. But when x = 1, the
morrell (mm59638) HW 11.7 radin (56025)
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001
10.0 points
Which, if any, of the following statements
are true?
A. If
morrell (mm59638) HW 11.9 radin (56025)
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001
1
On the other hand, since
lim |n cn|1/n = lim |cn |1/n ,
n
n
the Root