Calculus: An Applied Approach (Providence College: MTH 109)
9th Edition
ISBN: 9781285142616
Author: Ron Larson
Publisher: CENGAGE C
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Chapter A3, Problem 19E
To determine
To calculate: The value of the expression
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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 A3 Solutions
Calculus: An Applied Approach (Providence College: MTH 109)
Ch. A3 - Checkpoint 1 Worked-out solution available at...Ch. A3 - Prob. 2CPCh. A3 - Prob. 3CPCh. A3 - Prob. 4CPCh. A3 - Prob. 5CPCh. A3 - Prob. 6CPCh. A3 - Prob. 7CPCh. A3 - Prob. 1ECh. A3 - Prob. 2ECh. A3 - Prob. 3E
Ch. A3 - Prob. 4ECh. A3 - Prob. 5ECh. A3 - Prob. 6ECh. A3 - Prob. 7ECh. A3 - Prob. 8ECh. A3 - Prob. 9ECh. A3 - Prob. 10ECh. A3 - Prob. 11ECh. A3 - Prob. 12ECh. A3 - Prob. 13ECh. A3 - Prob. 14ECh. A3 - Prob. 15ECh. A3 - Prob. 16ECh. A3 - Prob. 17ECh. A3 - Evaluating Expressions In Exercises 1-20, evaluate...Ch. A3 - Prob. 19ECh. A3 - Prob. 20ECh. A3 - Prob. 21ECh. A3 - Prob. 22ECh. A3 - Prob. 23ECh. A3 - Prob. 24ECh. A3 - Simplifying Expressions with Exponents In...Ch. A3 - Prob. 26ECh. A3 - Prob. 27ECh. A3 - Prob. 28ECh. A3 - Prob. 29ECh. A3 - Prob. 30ECh. A3 - Prob. 31ECh. A3 - Prob. 32ECh. A3 - Prob. 33ECh. A3 - Prob. 34ECh. A3 - Prob. 35ECh. A3 - Prob. 36ECh. A3 - Prob. 37ECh. A3 - Prob. 38ECh. A3 - Prob. 39ECh. A3 - Prob. 40ECh. A3 - Prob. 41ECh. A3 - Prob. 42ECh. A3 - Prob. 43ECh. A3 - Prob. 44ECh. A3 - Prob. 45ECh. A3 - Prob. 46ECh. A3 - Prob. 47ECh. A3 - Prob. 48ECh. A3 - Prob. 49ECh. A3 - Prob. 50ECh. A3 - Prob. 51ECh. A3 - Prob. 52ECh. A3 - Prob. 53ECh. A3 - Prob. 54ECh. A3 - Prob. 55ECh. A3 - Prob. 56ECh. A3 - Prob. 57ECh. A3 - Prob. 58E
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