Precalculus Enhanced with Graphing Utilities (7th Edition)
7th Edition
ISBN: 9780134119281
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Chapter B, Problem 23SB
To determine
To find: Determine whether each sequence converges or diverges. If it converges, find its limit.
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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 B Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Ch. B - If a sequence { S n } converges to L , we call L...Ch. B - If a 1 , a 2 ,..., a n ,... is some collection of...Ch. B - Prob. 3CVCh. B - Prob. 4CVCh. B - Prob. 5SBCh. B - Prob. 6SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 10SB
Ch. B - Prob. 11SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 15SBCh. B - Prob. 16SBCh. B - Prob. 17SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 19SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 21SBCh. B - Prob. 22SBCh. B - Prob. 23SBCh. B - Prob. 24SBCh. B - Prob. 25SBCh. B - Prob. 26SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 29-32, find the first five terms in...Ch. B - In Problems 29-32, find the first five terms in...Ch. B - Prob. 31SBCh. B - In Problems 29-32, find the first five terms in...
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