Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Chapter 3.3, Problem 3PT
To determine
To choose: The appropriate option for the value of
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EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 3 Solutions
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Ch. 3.1 - Prob. 1PTCh. 3.1 - Prob. 2PTCh. 3.1 - Prob. 3PTCh. 3.1 - Prob. 4PTCh. 3.1 - Prob. 5PTCh. 3.1 - Prob. 6PTCh. 3.2 - Prob. 1PTCh. 3.2 - Prob. 2PTCh. 3.2 - Prob. 3PTCh. 3.2 - Prob. 4PT
Ch. 3.3 - Prob. 1PTCh. 3.3 - Prob. 2PTCh. 3.3 - Prob. 3PTCh. 3.3 - Prob. 4PTCh. 3.3 - Prob. 5PTCh. 3.3 - Prob. 6PTCh. 3.4 - Prob. 1PTCh. 3.4 - Prob. 2PTCh. 3.4 - Prob. 3PTCh. 3.4 - Prob. 4PTCh. 3.4 - Prob. 5PTCh. 3.4 - Prob. 6PTCh. 3.4 - Prob. 7PTCh. 3.5 - Prob. 1PTCh. 3.5 - Prob. 2PTCh. 3.5 - Prob. 3PTCh. 3.5 - Prob. 4PTCh. 3.5 - Prob. 5PTCh. 3.5 - Prob. 6PTCh. 3.6 - Prob. 1PTCh. 3.6 - Prob. 2PTCh. 3.6 - Prob. 3PTCh. 3.6 - Prob. 4PTCh. 3.6 - Prob. 5PTCh. 3.7 - Prob. 1PTCh. 3.7 - Prob. 2PTCh. 3.7 - Prob. 3PTCh. 3.7 - Prob. 4PTCh. 3.8 - Prob. 1PTCh. 3.8 - A bacteria culture starts with 50 organisms and...Ch. 3.8 - Prob. 3PTCh. 3.9 - A right triangle has one leg with constant length...Ch. 3.9 - Prob. 2PTCh. 3.10 - Prob. 1PTCh. 3.10 - Prob. 2PTCh. 3.10 - Prob. 3PTCh. 3.10 - Prob. 4PTCh. 3.11 - Prob. 1PTCh. 3.11 - Prob. 2PTCh. 3.11 - Prob. 3PTCh. 3.11 - Prob. 4PTCh. 3.11 - Prob. 5PT
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