Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Question
Chapter 4.5, Problem 50S
To determine
To find the exact value of the definite integral of given function.
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2
prove that Dxy #Dx Dy
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.
Chapter 4 Solutions
Calculus
Ch. 4.1 - Prob. 1TBCh. 4.1 - Prob. 2TBCh. 4.1 - Prob. 3TBCh. 4.1 - Prob. 0CCh. 4.1 - Prob. 1CCh. 4.1 - Prob. 2CCh. 4.1 - Prob. 3CCh. 4.1 - Prob. 4CCh. 4.1 - Prob. 5CCh. 4.1 - Prob. 6C
Ch. 4.1 - Prob. 7CCh. 4.1 - Prob. 8CCh. 4.1 - Prob. 9CCh. 4.1 - Prob. 10CCh. 4.1 - Prob. 11CCh. 4.1 - Prob. 12CCh. 4.1 - Prob. 13CCh. 4.1 - Prob. 14CCh. 4.1 - Prob. 15CCh. 4.1 - Prob. 16CCh. 4.1 - Prob. 17CCh. 4.1 - Prob. 18CCh. 4.1 - Prob. 19CCh. 4.1 - Prob. 20CCh. 4.1 - Prob. 21SCh. 4.1 - Prob. 22SCh. 4.1 - Prob. 23SCh. 4.1 - Prob. 24SCh. 4.1 - Prob. 25SCh. 4.1 - Prob. 26SCh. 4.1 - Prob. 27SCh. 4.1 - Prob. 28SCh. 4.1 - Prob. 29SCh. 4.1 - Prob. 30SCh. 4.1 - Prob. 31SCh. 4.1 - Prob. 32SCh. 4.1 - Prob. 33SCh. 4.1 - Prob. 34SCh. 4.1 - Prob. 35SCh. 4.1 - Prob. 36SCh. 4.1 - Prob. 37SCh. 4.1 - Prob. 38SCh. 4.1 - Prob. 39SCh. 4.1 - Prob. 40SCh. 4.1 - Prob. 41SCh. 4.1 - Prob. 42SCh. 4.1 - Prob. 43SCh. 4.1 - Prob. 44SCh. 4.1 - Prob. 45SCh. 4.1 - Prob. 46SCh. 4.1 - Prob. 47SCh. 4.1 - Prob. 48SCh. 4.1 - Prob. 49SCh. 4.1 - Prob. 50SCh. 4.1 - Prob. 51SCh. 4.1 - Prob. 52SCh. 4.1 - Prob. 53ACh. 4.1 - Prob. 54ACh. 4.1 - Prob. 55ACh. 4.1 - Prob. 56ACh. 4.1 - Prob. 57ACh. 4.1 - Prob. 58PCh. 4.1 - Prob. 59PCh. 4.1 - Prob. 60PCh. 4.1 - Prob. 61PCh. 4.1 - Prob. 62PCh. 4.1 - Prob. 1TFCh. 4.1 - Prob. 2TFCh. 4.1 - Prob. 3TFCh. 4.1 - Prob. 4TFCh. 4.1 - Prob. 5TFCh. 4.1 - Prob. 6TFCh. 4.1 - Prob. 7TFCh. 4.2 - Prob. 1TBCh. 4.2 - Prob. 0CCh. 4.2 - Prob. 1CCh. 4.2 - Prob. 2CCh. 4.2 - Prob. 3CCh. 4.2 - Prob. 4CCh. 4.2 - Prob. 5CCh. 4.2 - Prob. 6CCh. 4.2 - Prob. 7CCh. 4.2 - Prob. 8CCh. 4.2 - Prob. 9CCh. 4.2 - Prob. 10CCh. 4.2 - Prob. 11CCh. 4.2 - Prob. 12CCh. 4.2 - Prob. 13CCh. 4.2 - Prob. 14CCh. 4.2 - Prob. 15CCh. 4.2 - Prob. 16CCh. 4.2 - Prob. 17CCh. 4.2 - Prob. 18CCh. 4.2 - Prob. 19CCh. 4.2 - Prob. 20CCh. 4.2 - Prob. 21SCh. 4.2 - Prob. 22SCh. 4.2 - Prob. 23SCh. 4.2 - Prob. 24SCh. 4.2 - Prob. 25SCh. 4.2 - Prob. 26SCh. 4.2 - Prob. 27SCh. 4.2 - Prob. 28SCh. 4.2 - Prob. 29SCh. 4.2 - Prob. 30SCh. 4.2 - Prob. 31SCh. 4.2 - Prob. 32SCh. 4.2 - Prob. 33SCh. 4.2 - Prob. 34SCh. 4.2 - Prob. 35SCh. 4.2 - Prob. 36SCh. 4.2 - Prob. 37SCh. 4.2 - Prob. 38SCh. 4.2 - Prob. 39SCh. 4.2 - Prob. 40SCh. 4.2 - Prob. 41SCh. 4.2 - Prob. 42SCh. 4.2 - 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Prob. 30SCh. 4.3 - Prob. 31SCh. 4.3 - Prob. 32SCh. 4.3 - Prob. 33SCh. 4.3 - Prob. 34SCh. 4.3 - Prob. 35SCh. 4.3 - Prob. 36SCh. 4.3 - Prob. 37SCh. 4.3 - Prob. 38SCh. 4.3 - Prob. 39SCh. 4.3 - Prob. 40SCh. 4.3 - Prob. 41SCh. 4.3 - Prob. 42SCh. 4.3 - Prob. 43SCh. 4.3 - Prob. 44SCh. 4.3 - Prob. 45SCh. 4.3 - Prob. 46SCh. 4.3 - Prob. 47SCh. 4.3 - Prob. 48SCh. 4.3 - Prob. 49SCh. 4.3 - Prob. 50SCh. 4.3 - Prob. 51SCh. 4.3 - Prob. 52SCh. 4.3 - Prob. 53ACh. 4.3 - Prob. 54ACh. 4.3 - Prob. 55PCh. 4.3 - Prob. 56PCh. 4.3 - Prob. 57PCh. 4.3 - Prob. 58PCh. 4.3 - Prob. 59PCh. 4.3 - Prob. 60PCh. 4.3 - Prob. 61PCh. 4.3 - Prob. 62PCh. 4.3 - Prob. 1TFCh. 4.3 - Prob. 2TFCh. 4.3 - Prob. 3TFCh. 4.3 - Prob. 4TFCh. 4.4 - Prob. 1TBCh. 4.4 - Prob. 2TBCh. 4.4 - Prob. 3TBCh. 4.4 - Prob. 4TBCh. 4.4 - Prob. 0CCh. 4.4 - Prob. 1CCh. 4.4 - Prob. 2CCh. 4.4 - Prob. 3CCh. 4.4 - Prob. 4CCh. 4.4 - Prob. 5CCh. 4.4 - Prob. 6CCh. 4.4 - Prob. 7CCh. 4.4 - Prob. 8CCh. 4.4 - Prob. 9CCh. 4.4 - Prob. 10CCh. 4.4 - Prob. 11CCh. 4.4 - Prob. 12CCh. 4.4 - Prob. 13CCh. 4.4 - Prob. 14CCh. 4.4 - Prob. 15CCh. 4.4 - Prob. 16CCh. 4.4 - Prob. 17CCh. 4.4 - Prob. 18CCh. 4.4 - Prob. 19CCh. 4.4 - Prob. 20CCh. 4.4 - Prob. 21SCh. 4.4 - Prob. 22SCh. 4.4 - Prob. 23SCh. 4.4 - Prob. 24SCh. 4.4 - Prob. 25SCh. 4.4 - Prob. 26SCh. 4.4 - Prob. 27SCh. 4.4 - Prob. 28SCh. 4.4 - Prob. 29SCh. 4.4 - Prob. 30SCh. 4.4 - Prob. 31SCh. 4.4 - Prob. 32SCh. 4.4 - Prob. 33SCh. 4.4 - Prob. 34SCh. 4.4 - Prob. 35SCh. 4.4 - Prob. 36SCh. 4.4 - Prob. 37SCh. 4.4 - Prob. 38SCh. 4.4 - Prob. 39SCh. 4.4 - Prob. 40SCh. 4.4 - Prob. 41SCh. 4.4 - Prob. 42SCh. 4.4 - Prob. 43SCh. 4.4 - Prob. 44SCh. 4.4 - Prob. 45SCh. 4.4 - Prob. 46SCh. 4.4 - Prob. 47SCh. 4.4 - Prob. 48SCh. 4.4 - Prob. 49SCh. 4.4 - Prob. 50SCh. 4.4 - Prob. 51SCh. 4.4 - Prob. 52SCh. 4.4 - Prob. 53SCh. 4.4 - Prob. 54SCh. 4.4 - Prob. 55SCh. 4.4 - Prob. 56SCh. 4.4 - Prob. 57SCh. 4.4 - Prob. 58SCh. 4.4 - Prob. 59SCh. 4.4 - Prob. 60SCh. 4.4 - Prob. 61SCh. 4.4 - Prob. 62SCh. 4.4 - Prob. 63SCh. 4.4 - Prob. 64SCh. 4.4 - Prob. 65SCh. 4.4 - Prob. 66SCh. 4.4 - Prob. 67SCh. 4.4 - Prob. 68SCh. 4.4 - Prob. 69ACh. 4.4 - Prob. 70ACh. 4.4 - Prob. 71PCh. 4.4 - Prob. 72PCh. 4.4 - Prob. 73PCh. 4.4 - Prob. 74PCh. 4.4 - Prob. 75PCh. 4.4 - Prob. 76PCh. 4.4 - Prob. 77PCh. 4.4 - Prob. 78PCh. 4.4 - Prob. 79PCh. 4.4 - Prob. 1TFCh. 4.4 - Prob. 2TFCh. 4.4 - Prob. 3TFCh. 4.4 - Prob. 4TFCh. 4.4 - Prob. 5TFCh. 4.4 - Prob. 6TFCh. 4.4 - Prob. 7TFCh. 4.4 - Prob. 8TFCh. 4.4 - Prob. 9TFCh. 4.4 - Prob. 10TFCh. 4.5 - Prob. 1TBCh. 4.5 - Prob. 2TBCh. 4.5 - Prob. 3TBCh. 4.5 - Prob. 4TBCh. 4.5 - Prob. 0CCh. 4.5 - Prob. 1CCh. 4.5 - Prob. 2CCh. 4.5 - Prob. 3CCh. 4.5 - Prob. 4CCh. 4.5 - Prob. 5CCh. 4.5 - Prob. 6CCh. 4.5 - Prob. 7CCh. 4.5 - Prob. 8CCh. 4.5 - Prob. 9CCh. 4.5 - Prob. 10CCh. 4.5 - Prob. 11CCh. 4.5 - Prob. 12CCh. 4.5 - Prob. 13CCh. 4.5 - Prob. 14CCh. 4.5 - Prob. 15CCh. 4.5 - Prob. 16CCh. 4.5 - Prob. 17CCh. 4.5 - Prob. 18CCh. 4.5 - Prob. 19SCh. 4.5 - Prob. 20SCh. 4.5 - Prob. 21SCh. 4.5 - Prob. 22SCh. 4.5 - Prob. 23SCh. 4.5 - Prob. 24SCh. 4.5 - Prob. 25SCh. 4.5 - Prob. 26SCh. 4.5 - Prob. 27SCh. 4.5 - Prob. 28SCh. 4.5 - Prob. 29SCh. 4.5 - Prob. 30SCh. 4.5 - Prob. 31SCh. 4.5 - Prob. 32SCh. 4.5 - Prob. 33SCh. 4.5 - Prob. 34SCh. 4.5 - Prob. 35SCh. 4.5 - Prob. 36SCh. 4.5 - Prob. 37SCh. 4.5 - Prob. 38SCh. 4.5 - Prob. 39SCh. 4.5 - Prob. 40SCh. 4.5 - Prob. 41SCh. 4.5 - Prob. 42SCh. 4.5 - Prob. 43SCh. 4.5 - Prob. 44SCh. 4.5 - Prob. 45SCh. 4.5 - Prob. 46SCh. 4.5 - Prob. 47SCh. 4.5 - Prob. 48SCh. 4.5 - Prob. 49SCh. 4.5 - Prob. 50SCh. 4.5 - Prob. 51SCh. 4.5 - Prob. 52SCh. 4.5 - Prob. 53SCh. 4.5 - Prob. 54SCh. 4.5 - Prob. 55SCh. 4.5 - Prob. 56SCh. 4.5 - Prob. 57SCh. 4.5 - Prob. 58SCh. 4.5 - Prob. 59SCh. 4.5 - Prob. 60SCh. 4.5 - Prob. 61SCh. 4.5 - Prob. 62SCh. 4.5 - Prob. 63SCh. 4.5 - Prob. 64SCh. 4.5 - Prob. 65ACh. 4.5 - Prob. 66ACh. 4.5 - Prob. 67ACh. 4.5 - Prob. 68ACh. 4.5 - Prob. 69ACh. 4.5 - Prob. 70ACh. 4.5 - Prob. 71ACh. 4.5 - Prob. 72PCh. 4.5 - Prob. 73PCh. 4.5 - Prob. 74PCh. 4.5 - Prob. 75PCh. 4.5 - Prob. 76PCh. 4.5 - Prob. 77PCh. 4.5 - Prob. 78PCh. 4.5 - Prob. 79PCh. 4.5 - Prob. 80PCh. 4.5 - Prob. 1TFCh. 4.5 - Prob. 2TFCh. 4.5 - Prob. 3TFCh. 4.5 - Prob. 4TFCh. 4.5 - Prob. 5TFCh. 4.5 - Prob. 6TFCh. 4.6 - Prob. 1TBCh. 4.6 - Prob. 2TBCh. 4.6 - Prob. 3TBCh. 4.6 - Prob. 4TBCh. 4.6 - Prob. 5TBCh. 4.6 - Prob. 0CCh. 4.6 - Prob. 1CCh. 4.6 - Prob. 2CCh. 4.6 - Prob. 3CCh. 4.6 - Prob. 4CCh. 4.6 - Prob. 5CCh. 4.6 - Prob. 6CCh. 4.6 - Prob. 7CCh. 4.6 - Prob. 8CCh. 4.6 - Prob. 9CCh. 4.6 - Prob. 10CCh. 4.6 - Prob. 11CCh. 4.6 - Prob. 12CCh. 4.6 - Prob. 13CCh. 4.6 - Prob. 14CCh. 4.6 - Prob. 15CCh. 4.6 - Prob. 16CCh. 4.6 - Prob. 17CCh. 4.6 - Prob. 18CCh. 4.6 - Prob. 19CCh. 4.6 - Prob. 20CCh. 4.6 - Prob. 21CCh. 4.6 - Prob. 22CCh. 4.6 - Prob. 23SCh. 4.6 - Prob. 24SCh. 4.6 - Prob. 25SCh. 4.6 - Prob. 26SCh. 4.6 - Prob. 27SCh. 4.6 - Prob. 28SCh. 4.6 - Prob. 29SCh. 4.6 - Prob. 30SCh. 4.6 - Prob. 31SCh. 4.6 - Prob. 32SCh. 4.6 - Prob. 33SCh. 4.6 - Prob. 34SCh. 4.6 - Prob. 35SCh. 4.6 - Prob. 36SCh. 4.6 - Prob. 37SCh. 4.6 - Prob. 38SCh. 4.6 - Prob. 39SCh. 4.6 - Prob. 40SCh. 4.6 - Prob. 41SCh. 4.6 - Prob. 42SCh. 4.6 - Prob. 43SCh. 4.6 - Prob. 44SCh. 4.6 - Prob. 45SCh. 4.6 - Prob. 46SCh. 4.6 - Prob. 47SCh. 4.6 - Prob. 48SCh. 4.6 - Prob. 49SCh. 4.6 - Prob. 50SCh. 4.6 - Prob. 51SCh. 4.6 - Prob. 52SCh. 4.6 - Prob. 53SCh. 4.6 - Prob. 54SCh. 4.6 - Prob. 55SCh. 4.6 - Prob. 56SCh. 4.6 - Prob. 57SCh. 4.6 - Prob. 58SCh. 4.6 - Prob. 59SCh. 4.6 - Prob. 60SCh. 4.6 - Prob. 61SCh. 4.6 - Prob. 62SCh. 4.6 - Prob. 63SCh. 4.6 - Prob. 64SCh. 4.6 - Prob. 65SCh. 4.6 - Prob. 66SCh. 4.6 - Prob. 67SCh. 4.6 - Prob. 68SCh. 4.6 - Prob. 69SCh. 4.6 - Prob. 70SCh. 4.6 - Prob. 71SCh. 4.6 - Prob. 72SCh. 4.6 - Prob. 73SCh. 4.6 - Prob. 74ACh. 4.6 - Prob. 75ACh. 4.6 - Prob. 76ACh. 4.6 - Prob. 77ACh. 4.6 - Prob. 78PCh. 4.6 - Prob. 79PCh. 4.6 - Prob. 80PCh. 4.6 - Prob. 81PCh. 4.6 - Prob. 82PCh. 4.6 - Prob. 1TFCh. 4.6 - Prob. 2TFCh. 4.6 - Prob. 3TFCh. 4.6 - Prob. 4TFCh. 4.6 - Prob. 5TFCh. 4.7 - Prob. 1TBCh. 4.7 - Prob. 2TBCh. 4.7 - Prob. 3TBCh. 4.7 - Prob. 0CCh. 4.7 - Prob. 1CCh. 4.7 - Prob. 2CCh. 4.7 - 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Prob. 56SCh. 4.7 - Prob. 57SCh. 4.7 - Prob. 58SCh. 4.7 - Prob. 59ACh. 4.7 - Prob. 60ACh. 4.7 - Prob. 61ACh. 4.7 - Prob. 62ACh. 4.7 - Prob. 63PCh. 4.7 - Prob. 64PCh. 4.7 - Prob. 65PCh. 4.7 - Prob. 66PCh. 4.7 - Prob. 67PCh. 4.7 - Prob. 68PCh. 4.7 - Prob. 69PCh. 4.7 - Prob. 70PCh. 4.7 - Prob. 71PCh. 4.7 - Prob. 72PCh. 4.7 - Prob. 73PCh. 4.7 - Prob. 74PCh. 4.7 - Prob. 75PCh. 4.7 - Prob. 76PCh. 4.7 - Prob. 77PCh. 4.7 - Prob. 78PCh. 4.7 - Prob. 1TFCh. 4.7 - Prob. 2TFCh. 4.7 - Prob. 3TFCh. 4.7 - Prob. 4TFCh. 4.7 - Prob. 5TFCh. 4.7 - Prob. 6TFCh. 4.7 - Prob. 7TFCh. 4.7 - Prob. 8TFCh. 4 - Prob. 1DCh. 4 - Prob. 2DCh. 4 - Prob. 3DCh. 4 - Prob. 4DCh. 4 - Prob. 5DCh. 4 - Prob. 6DCh. 4 - Prob. 7DCh. 4 - Prob. 8DCh. 4 - Prob. 9DCh. 4 - Prob. 10DCh. 4 - Prob. 11DCh. 4 - Prob. 12DCh. 4 - Prob. 13DCh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - Prob. 13TCh. 4 - 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Prob. 52NFARCh. 4 - Prob. 53NFARCh. 4 - Prob. 54NFARCh. 4 - Prob. 1SCCh. 4 - Prob. 2SCCh. 4 - Prob. 3SCCh. 4 - Prob. 4SCCh. 4 - Prob. 5SCCh. 4 - Prob. 6SCCh. 4 - Prob. 7SCCh. 4 - Prob. 8SCCh. 4 - Prob. 9SCCh. 4 - Prob. 10SCCh. 4 - Prob. 11SCCh. 4 - Prob. 12SCCh. 4 - Prob. 13SCCh. 4 - Prob. 14SCCh. 4 - Prob. 15SCCh. 4 - Prob. 16SCCh. 4 - Prob. 17SCCh. 4 - Prob. 18SCCh. 4 - Prob. 19SCCh. 4 - Prob. 20SCCh. 4 - Prob. 21SCCh. 4 - Prob. 22SCCh. 4 - Prob. 23SCCh. 4 - Prob. 24SCCh. 4 - Prob. 25SCCh. 4 - Prob. 26SCCh. 4 - Prob. 27SCCh. 4 - Prob. 28SCCh. 4 - Prob. 29SCCh. 4 - Prob. 30SCCh. 4 - Prob. 31SCCh. 4 - Prob. 32SCCh. 4 - Prob. 33SCCh. 4 - Prob. 34SCCh. 4 - Prob. 35SCCh. 4 - Prob. 36SCCh. 4 - Prob. 37SCCh. 4 - Prob. 38SCCh. 4 - Prob. 39SCCh. 4 - Prob. 40SCCh. 4 - Prob. 41SCCh. 4 - Prob. 42SCCh. 4 - Prob. 43SCCh. 4 - Prob. 44SCCh. 4 - Prob. 45SCCh. 4 - Prob. 46SCCh. 4 - Prob. 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Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Chain Rule dy:dx = dy:du*du:dx; Author: Robert Cappetta;https://www.youtube.com/watch?v=IUYniALwbHs;License: Standard YouTube License, CC-BY
CHAIN RULE Part 1; Author: Btech Maths Hub;https://www.youtube.com/watch?v=TIAw6AJ_5Po;License: Standard YouTube License, CC-BY