zakaria (mmz255) HW15 gilbert (55485)
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001
002
x
x y
0
0
2 xy 2 dxdydz
I=
(3x + 2y ) dzdydx .
E
0
when E is the set
The Required Sentence for the Test for Divergence
Whenever you apply the TEST FOR DIVERGENCE to conclude that the series
a
n 1
is Divergent,
n
you must, with regard to the SEQUENCE OF TERMS a1 , a2 , a3 , a4 , a5 , .
(and not with regard to the SEQUENCE O
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Problem #1:
(a) Find T 3 , the n = 3 Taylor Polynomial at a = 1 of f(x) = In x .
(b) Determine T3 (1.1).
(c) Show that T3 (1.1) % 111(1 _ 1) is correct to 4 decimal places.
(1) Show that T3 (x) m I
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P( x)
Q( x)
Finding the Partial Fraction Decomposition (PFD) of
when the deg P(x) < deg Q(x) :
1) Identify the Basic Form of the PFD (factor Q(x) as far as possible)
2) Write Equation:
P( x)
Q( x)
= Basic Form
3) Multiply by Q(x) and solve for the unknown
Integrating Powers and Products of Trig functions
Review of Techniques
In all of the formulas below, m, n, k, and t are all positive integers .
I. Strategy for Integrating
(sin
m
x) (cos n x) dx
A. If n is odd,
use u = sin x , du = cos x dx and write all
parga (jrp3484) HW15 radin (55095)
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001
1
Thus the critical points of A(x) occur at
5
x = ,
2
5
,
2
only one of whic
parga (jrp3484) HW17 radin (55095)
1
y
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001
R2
10.0 points
a
Use properties of integrals to determine the
value of
c
parga (jrp3484) HW18 radin (55095)
1
4
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001
2.
3
2
2
1
0
10.0 points
-1
2
-2
A function h has graph
2
2
-3
-4
3
3.
2
parga (jrp3484) HW19 radin (55095)
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001
1
keywords: IntSubst, IntSubstExam,
002
10.0 points
Evaluate the integral
10
parga (jrp3484) HW20 radin (55095)
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001
6
4.
4
2
10.0 points
2
For which one of the following shaded regions is its
parga (jrp3484) HW21 radin (55095)
This print-out should have 17 questions.
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1
5
1
+C
ln x
3 x2
2
5. I =
001
4. I =
1
5
+C
ln x +
2
2x
2
10.0 points
Evaluat
parga (jrp3484) HW22 radin (55095)
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001
In this case,
1
(1 + 2x2 ) dx =
I=
0
I=
0
2
x + x3
3
1
0
.
Consequently
10.0
parga (jrp3484) HW23 radin (55095)
This print-out should have 15 questions.
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001
keywords:
002
1
dx .
+ 1)3/2
1. I = ln x
1. I = 1
3. I =
1
3
x2 1
x2 1 + C
parga (jrp3484) HW24 radin (55095)
This print-out should have 16 questions.
Multiple-choice questions may continue on
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before answering.
Note that this last HW is due Monday 12/3,
9pm. Midterm 3 is Tuesday 12/4 in cla
parga (jrp3484) HW16 radin (55095)
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001
with C an arbitrary constant.
002
f (t) = 6(3t + 1)
Find all functions g suc