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Calculus Combo
14th Edition
ISBN: 9781464151088
Author: Associate Professor Laura Taalman, Peter Kohn
Publisher: W.H. Freeman & Company
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Concept explainers
Question
Chapter 2.3, Problem 92P
To determine
To prove: that if g(x) and h(x) are continuous and differentiable at x=c , and if g(c)=h(c) and g′(c)=h′(c) , then f is differentiable at x=c .
Expert Solution & Answer
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Students have asked these similar questions
Evaluate the definite integral using the given integration limits and the limits obtained by trigonometric substitution.
14
x²
dx
249
(a) the given integration limits
(b) the limits obtained by trigonometric substitution
Assignment #1
Q1: Test the following series for convergence. Specify the test you use:
1
n+5
(-1)n
a) Σn=o
√n²+1
b) Σn=1 n√n+3
c) Σn=1 (2n+1)3
3n
1
d) Σn=1 3n-1
e) Σn=1
4+4n
answer problem 1a, 1b, 1c, 1d, and 1e and show work/ explain how you got the answer
Chapter 2 Solutions
Calculus Combo
Ch. 2.1 - Prob. 1TBCh. 2.1 - Prob. 2TBCh. 2.1 - Prob. 3TBCh. 2.1 - Prob. 4TBCh. 2.1 - Prob. 0CCh. 2.1 - Prob. 1CCh. 2.1 - Prob. 2CCh. 2.1 - Prob. 3CCh. 2.1 - Prob. 4CCh. 2.1 - Prob. 5C
Ch. 2.1 - Prob. 6CCh. 2.1 - Prob. 7CCh. 2.1 - Prob. 8CCh. 2.1 - Prob. 9CCh. 2.1 - Prob. 10CCh. 2.1 - Prob. 11CCh. 2.1 - Prob. 12CCh. 2.1 - Prob. 13CCh. 2.1 - Prob. 14CCh. 2.1 - Prob. 15CCh. 2.1 - Prob. 16CCh. 2.1 - Prob. 17CCh. 2.1 - Prob. 18CCh. 2.1 - Prob. 19CCh. 2.1 - Prob. 20CCh. 2.1 - Prob. 21SCh. 2.1 - Prob. 22SCh. 2.1 - Prob. 23SCh. 2.1 - Prob. 24SCh. 2.1 - Prob. 25SCh. 2.1 - Prob. 26SCh. 2.1 - Prob. 27SCh. 2.1 - Prob. 28SCh. 2.1 - Prob. 29SCh. 2.1 - Prob. 30SCh. 2.1 - Prob. 31SCh. 2.1 - Prob. 32SCh. 2.1 - Prob. 33SCh. 2.1 - Prob. 34SCh. 2.1 - Prob. 35SCh. 2.1 - Prob. 36SCh. 2.1 - Prob. 37SCh. 2.1 - Prob. 38SCh. 2.1 - Prob. 39SCh. 2.1 - Prob. 40SCh. 2.1 - Prob. 41SCh. 2.1 - Prob. 42SCh. 2.1 - Prob. 43SCh. 2.1 - Prob. 44SCh. 2.1 - Prob. 45ACh. 2.1 - Prob. 46ACh. 2.1 - Prob. 47ACh. 2.1 - Prob. 48ACh. 2.1 - Prob. 49ACh. 2.1 - Prob. 50ACh. 2.1 - Prob. 51ACh. 2.1 - Prob. 52ACh. 2.1 - Prob. 53ACh. 2.1 - Prob. 54ACh. 2.1 - Prob. 55ACh. 2.1 - Prob. 56ACh. 2.1 - Prob. 57ACh. 2.1 - Prob. 58PCh. 2.1 - Prob. 59PCh. 2.1 - Prob. 1TFCh. 2.1 - Prob. 2TFCh. 2.1 - Prob. 3TFCh. 2.2 - Prob. 1TBCh. 2.2 - Prob. 2TBCh. 2.2 - Prob. 0CCh. 2.2 - Prob. 1CCh. 2.2 - Prob. 2CCh. 2.2 - Prob. 3CCh. 2.2 - Prob. 4CCh. 2.2 - Prob. 5CCh. 2.2 - Prob. 6CCh. 2.2 - Prob. 7CCh. 2.2 - Prob. 8CCh. 2.2 - Prob. 9CCh. 2.2 - Prob. 10CCh. 2.2 - Prob. 11CCh. 2.2 - Prob. 12CCh. 2.2 - Prob. 13CCh. 2.2 - Prob. 14CCh. 2.2 - Prob. 15CCh. 2.2 - Prob. 16CCh. 2.2 - Prob. 17CCh. 2.2 - Prob. 18CCh. 2.2 - Prob. 19CCh. 2.2 - Prob. 20CCh. 2.2 - Prob. 21CCh. 2.2 - Prob. 22CCh. 2.2 - Prob. 23SCh. 2.2 - Prob. 24SCh. 2.2 - Prob. 25SCh. 2.2 - Prob. 26SCh. 2.2 - Prob. 27SCh. 2.2 - Prob. 28SCh. 2.2 - Prob. 29SCh. 2.2 - Prob. 30SCh. 2.2 - Prob. 31SCh. 2.2 - Prob. 32SCh. 2.2 - Prob. 33SCh. 2.2 - Prob. 34SCh. 2.2 - Prob. 35SCh. 2.2 - Prob. 36SCh. 2.2 - Prob. 37SCh. 2.2 - Prob. 38SCh. 2.2 - Prob. 39SCh. 2.2 - Prob. 40SCh. 2.2 - Prob. 41SCh. 2.2 - Prob. 42SCh. 2.2 - Prob. 43SCh. 2.2 - Prob. 44SCh. 2.2 - Prob. 45SCh. 2.2 - Prob. 46SCh. 2.2 - Prob. 47SCh. 2.2 - Prob. 48SCh. 2.2 - Prob. 49SCh. 2.2 - Prob. 50SCh. 2.2 - Prob. 51SCh. 2.2 - Prob. 52SCh. 2.2 - Prob. 53SCh. 2.2 - Prob. 54SCh. 2.2 - Prob. 55SCh. 2.2 - Prob. 56SCh. 2.2 - Prob. 57SCh. 2.2 - Prob. 58SCh. 2.2 - Prob. 59SCh. 2.2 - Prob. 60SCh. 2.2 - Prob. 61SCh. 2.2 - Prob. 62SCh. 2.2 - Prob. 63SCh. 2.2 - Prob. 64SCh. 2.2 - Prob. 65SCh. 2.2 - Prob. 66SCh. 2.2 - Prob. 67SCh. 2.2 - Prob. 68SCh. 2.2 - Prob. 69SCh. 2.2 - Prob. 70SCh. 2.2 - Prob. 71SCh. 2.2 - Prob. 72SCh. 2.2 - Prob. 73SCh. 2.2 - Prob. 74SCh. 2.2 - Prob. 75SCh. 2.2 - Prob. 76SCh. 2.2 - Prob. 77SCh. 2.2 - Prob. 78SCh. 2.2 - Prob. 79SCh. 2.2 - Prob. 80SCh. 2.2 - Prob. 81SCh. 2.2 - Prob. 82SCh. 2.2 - Prob. 83SCh. 2.2 - Prob. 84SCh. 2.2 - Prob. 85SCh. 2.2 - Prob. 86SCh. 2.2 - Prob. 87ACh. 2.2 - Prob. 88ACh. 2.2 - Prob. 89ACh. 2.2 - Prob. 90ACh. 2.2 - Prob. 91ACh. 2.2 - Prob. 92PCh. 2.2 - Prob. 93PCh. 2.2 - Prob. 94PCh. 2.2 - Prob. 95PCh. 2.2 - Prob. 96PCh. 2.2 - Prob. 97PCh. 2.2 - Prob. 98PCh. 2.2 - Prob. 1TFCh. 2.2 - Prob. 2TFCh. 2.2 - Prob. 3TFCh. 2.2 - Prob. 4TFCh. 2.2 - Prob. 5TFCh. 2.3 - Prob. 1TBCh. 2.3 - Prob. 2TBCh. 2.3 - Prob. 3TBCh. 2.3 - Prob. 0CCh. 2.3 - Prob. 1CCh. 2.3 - Prob. 2CCh. 2.3 - Prob. 3CCh. 2.3 - Prob. 4CCh. 2.3 - Prob. 5CCh. 2.3 - Prob. 6CCh. 2.3 - Prob. 7CCh. 2.3 - Prob. 8CCh. 2.3 - Prob. 9CCh. 2.3 - Prob. 10CCh. 2.3 - Prob. 11CCh. 2.3 - Prob. 12CCh. 2.3 - Prob. 13CCh. 2.3 - Prob. 14CCh. 2.3 - Prob. 15CCh. 2.3 - Prob. 16CCh. 2.3 - Prob. 17CCh. 2.3 - Prob. 18CCh. 2.3 - Prob. 19CCh. 2.3 - Prob. 20CCh. 2.3 - Prob. 21CCh. 2.3 - Prob. 22CCh. 2.3 - Prob. 23SCh. 2.3 - Prob. 24SCh. 2.3 - Prob. 25SCh. 2.3 - Prob. 26SCh. 2.3 - Prob. 27SCh. 2.3 - Prob. 28SCh. 2.3 - Prob. 29SCh. 2.3 - Prob. 30SCh. 2.3 - Prob. 31SCh. 2.3 - Prob. 32SCh. 2.3 - Prob. 33SCh. 2.3 - Prob. 34SCh. 2.3 - Prob. 35SCh. 2.3 - Prob. 36SCh. 2.3 - Prob. 37SCh. 2.3 - Prob. 38SCh. 2.3 - Prob. 39SCh. 2.3 - Prob. 40SCh. 2.3 - Prob. 41SCh. 2.3 - Prob. 42SCh. 2.3 - Prob. 43SCh. 2.3 - Prob. 44SCh. 2.3 - Prob. 45SCh. 2.3 - Prob. 46SCh. 2.3 - Prob. 47SCh. 2.3 - Prob. 48SCh. 2.3 - Prob. 49SCh. 2.3 - Prob. 50SCh. 2.3 - Prob. 51SCh. 2.3 - Prob. 52SCh. 2.3 - Prob. 53SCh. 2.3 - Prob. 54SCh. 2.3 - Prob. 55SCh. 2.3 - Prob. 56SCh. 2.3 - Prob. 57SCh. 2.3 - Prob. 58SCh. 2.3 - Prob. 59SCh. 2.3 - Prob. 60SCh. 2.3 - Prob. 61SCh. 2.3 - Prob. 62SCh. 2.3 - Prob. 63SCh. 2.3 - Prob. 64SCh. 2.3 - Prob. 65SCh. 2.3 - Prob. 66SCh. 2.3 - Prob. 67SCh. 2.3 - Prob. 68SCh. 2.3 - Prob. 69SCh. 2.3 - Prob. 70SCh. 2.3 - Prob. 71SCh. 2.3 - Prob. 72SCh. 2.3 - Prob. 73SCh. 2.3 - Prob. 74SCh. 2.3 - Prob. 75SCh. 2.3 - Prob. 76SCh. 2.3 - Prob. 77SCh. 2.3 - Prob. 78SCh. 2.3 - Prob. 79ACh. 2.3 - Prob. 80ACh. 2.3 - Prob. 81ACh. 2.3 - Prob. 82ACh. 2.3 - Prob. 83ACh. 2.3 - Prob. 84PCh. 2.3 - Prob. 85PCh. 2.3 - Prob. 86PCh. 2.3 - Prob. 87PCh. 2.3 - Prob. 88PCh. 2.3 - Prob. 89PCh. 2.3 - Prob. 90PCh. 2.3 - Prob. 91PCh. 2.3 - Prob. 92PCh. 2.3 - Prob. 1TFCh. 2.3 - Prob. 2TFCh. 2.3 - Prob. 3TFCh. 2.3 - Prob. 4TFCh. 2.3 - Prob. 5TFCh. 2.4 - Prob. 1TBCh. 2.4 - Prob. 2TBCh. 2.4 - Prob. 0CCh. 2.4 - Prob. 1CCh. 2.4 - Prob. 2CCh. 2.4 - Prob. 3CCh. 2.4 - Prob. 4CCh. 2.4 - Prob. 5CCh. 2.4 - Prob. 6CCh. 2.4 - Prob. 7CCh. 2.4 - Prob. 8CCh. 2.4 - Prob. 9CCh. 2.4 - Prob. 10CCh. 2.4 - Prob. 11CCh. 2.4 - Prob. 12CCh. 2.4 - Prob. 13CCh. 2.4 - Prob. 14CCh. 2.4 - Prob. 15CCh. 2.4 - Prob. 16CCh. 2.4 - Prob. 17CCh. 2.4 - Prob. 18CCh. 2.4 - Prob. 19CCh. 2.4 - Prob. 20CCh. 2.4 - Prob. 21SCh. 2.4 - Prob. 22SCh. 2.4 - Prob. 23SCh. 2.4 - Prob. 24SCh. 2.4 - Prob. 25SCh. 2.4 - Prob. 26SCh. 2.4 - Prob. 27SCh. 2.4 - Prob. 28SCh. 2.4 - Prob. 29SCh. 2.4 - Prob. 30SCh. 2.4 - Prob. 31SCh. 2.4 - Prob. 32SCh. 2.4 - Prob. 33SCh. 2.4 - Prob. 34SCh. 2.4 - Prob. 35SCh. 2.4 - Prob. 36SCh. 2.4 - Prob. 37SCh. 2.4 - Prob. 38SCh. 2.4 - Prob. 39SCh. 2.4 - Prob. 40SCh. 2.4 - Prob. 41SCh. 2.4 - Prob. 42SCh. 2.4 - Prob. 43SCh. 2.4 - Prob. 44SCh. 2.4 - Prob. 45SCh. 2.4 - Prob. 46SCh. 2.4 - Prob. 47SCh. 2.4 - Prob. 48SCh. 2.4 - Prob. 49SCh. 2.4 - Prob. 50SCh. 2.4 - Prob. 51SCh. 2.4 - Prob. 52SCh. 2.4 - Prob. 53SCh. 2.4 - Prob. 54SCh. 2.4 - Prob. 55SCh. 2.4 - Prob. 56SCh. 2.4 - Prob. 57SCh. 2.4 - Prob. 58SCh. 2.4 - Prob. 59SCh. 2.4 - Prob. 60SCh. 2.4 - Prob. 61SCh. 2.4 - Prob. 62SCh. 2.4 - Prob. 63SCh. 2.4 - Prob. 64SCh. 2.4 - Prob. 65SCh. 2.4 - Prob. 66SCh. 2.4 - Prob. 67SCh. 2.4 - Prob. 68SCh. 2.4 - Prob. 69SCh. 2.4 - Prob. 70SCh. 2.4 - Prob. 71SCh. 2.4 - Prob. 72SCh. 2.4 - Prob. 73SCh. 2.4 - Prob. 74SCh. 2.4 - Prob. 75SCh. 2.4 - Prob. 76SCh. 2.4 - Prob. 77SCh. 2.4 - Prob. 78SCh. 2.4 - Prob. 79SCh. 2.4 - Prob. 80SCh. 2.4 - Prob. 81SCh. 2.4 - Prob. 82SCh. 2.4 - Prob. 83SCh. 2.4 - Prob. 84SCh. 2.4 - Prob. 85ACh. 2.4 - Prob. 86ACh. 2.4 - Prob. 87ACh. 2.4 - Prob. 88PCh. 2.4 - Prob. 89PCh. 2.4 - Prob. 90PCh. 2.4 - Prob. 91PCh. 2.4 - Prob. 92PCh. 2.4 - Prob. 93PCh. 2.4 - Prob. 94PCh. 2.4 - Prob. 1TFCh. 2.4 - Prob. 2TFCh. 2.4 - Prob. 3TFCh. 2.4 - Prob. 4TFCh. 2.4 - Prob. 5TFCh. 2.4 - Prob. 6TFCh. 2.4 - Prob. 7TFCh. 2.4 - Prob. 8TFCh. 2.4 - Prob. 9TFCh. 2.4 - Prob. 10TFCh. 2.5 - Prob. 1TBCh. 2.5 - Prob. 2TBCh. 2.5 - Prob. 0CCh. 2.5 - Prob. 1CCh. 2.5 - Prob. 2CCh. 2.5 - Prob. 3CCh. 2.5 - Prob. 4CCh. 2.5 - Prob. 5CCh. 2.5 - Prob. 6CCh. 2.5 - Prob. 7CCh. 2.5 - Prob. 8CCh. 2.5 - Prob. 9CCh. 2.5 - Prob. 10CCh. 2.5 - Prob. 11CCh. 2.5 - Prob. 12CCh. 2.5 - Prob. 13CCh. 2.5 - Prob. 14CCh. 2.5 - Prob. 15CCh. 2.5 - Prob. 16CCh. 2.5 - Prob. 17SCh. 2.5 - Prob. 18SCh. 2.5 - Prob. 19SCh. 2.5 - Prob. 20SCh. 2.5 - Prob. 21SCh. 2.5 - Prob. 22SCh. 2.5 - Prob. 23SCh. 2.5 - Prob. 24SCh. 2.5 - Prob. 25SCh. 2.5 - Prob. 26SCh. 2.5 - Prob. 27SCh. 2.5 - Prob. 28SCh. 2.5 - Prob. 29SCh. 2.5 - Prob. 30SCh. 2.5 - Prob. 31SCh. 2.5 - Prob. 32SCh. 2.5 - Prob. 33SCh. 2.5 - Prob. 34SCh. 2.5 - Prob. 35SCh. 2.5 - Prob. 36SCh. 2.5 - Prob. 37SCh. 2.5 - Prob. 38SCh. 2.5 - Prob. 39SCh. 2.5 - Prob. 40SCh. 2.5 - Prob. 41SCh. 2.5 - Prob. 42SCh. 2.5 - Prob. 43SCh. 2.5 - Prob. 44SCh. 2.5 - Prob. 45SCh. 2.5 - Prob. 46SCh. 2.5 - Prob. 47SCh. 2.5 - Prob. 48SCh. 2.5 - Prob. 49SCh. 2.5 - Prob. 50SCh. 2.5 - Prob. 51SCh. 2.5 - Prob. 52SCh. 2.5 - Prob. 53SCh. 2.5 - Prob. 54SCh. 2.5 - Prob. 55SCh. 2.5 - Prob. 56SCh. 2.5 - Prob. 57SCh. 2.5 - Prob. 58SCh. 2.5 - Prob. 59SCh. 2.5 - Prob. 60SCh. 2.5 - Prob. 61SCh. 2.5 - Prob. 62SCh. 2.5 - Prob. 63SCh. 2.5 - Prob. 64ACh. 2.5 - Prob. 65ACh. 2.5 - Prob. 66ACh. 2.5 - Prob. 67ACh. 2.5 - Prob. 68PCh. 2.5 - Prob. 69PCh. 2.5 - Prob. 70PCh. 2.5 - Prob. 71PCh. 2.5 - Prob. 72PCh. 2.5 - Prob. 73PCh. 2.5 - Prob. 74PCh. 2.5 - Prob. 1TFCh. 2.5 - Prob. 2TFCh. 2.5 - Prob. 3TFCh. 2.5 - Prob. 4TFCh. 2.5 - Prob. 5TFCh. 2.5 - Prob. 6TFCh. 2.5 - Prob. 7TFCh. 2.6 - Prob. 1TBCh. 2.6 - Prob. 2TBCh. 2.6 - Prob. 3TBCh. 2.6 - Prob. 0CCh. 2.6 - Prob. 1CCh. 2.6 - Prob. 2CCh. 2.6 - Prob. 3CCh. 2.6 - Prob. 4CCh. 2.6 - Prob. 5CCh. 2.6 - Prob. 6CCh. 2.6 - Prob. 7CCh. 2.6 - Prob. 8CCh. 2.6 - Prob. 9CCh. 2.6 - Prob. 10CCh. 2.6 - Prob. 11CCh. 2.6 - Prob. 12CCh. 2.6 - Prob. 13CCh. 2.6 - Prob. 14CCh. 2.6 - Prob. 15CCh. 2.6 - Prob. 16CCh. 2.6 - Prob. 17SCh. 2.6 - Prob. 18SCh. 2.6 - Prob. 19SCh. 2.6 - Prob. 20SCh. 2.6 - Prob. 21SCh. 2.6 - Prob. 22SCh. 2.6 - Prob. 23SCh. 2.6 - Prob. 24SCh. 2.6 - Prob. 25SCh. 2.6 - Prob. 26SCh. 2.6 - Prob. 27SCh. 2.6 - Prob. 28SCh. 2.6 - Prob. 29SCh. 2.6 - Prob. 30SCh. 2.6 - Prob. 31SCh. 2.6 - Prob. 32SCh. 2.6 - Prob. 33SCh. 2.6 - Prob. 34SCh. 2.6 - Prob. 35SCh. 2.6 - Prob. 36SCh. 2.6 - Prob. 37SCh. 2.6 - Prob. 38SCh. 2.6 - Prob. 39SCh. 2.6 - Prob. 40SCh. 2.6 - Prob. 41SCh. 2.6 - Prob. 42SCh. 2.6 - Prob. 43SCh. 2.6 - Prob. 44SCh. 2.6 - Prob. 45SCh. 2.6 - Prob. 46SCh. 2.6 - Prob. 47SCh. 2.6 - Prob. 48SCh. 2.6 - Prob. 49SCh. 2.6 - Prob. 50SCh. 2.6 - Prob. 51SCh. 2.6 - Prob. 52SCh. 2.6 - Prob. 53SCh. 2.6 - Prob. 54SCh. 2.6 - Prob. 55SCh. 2.6 - Prob. 56SCh. 2.6 - Prob. 57SCh. 2.6 - Prob. 58SCh. 2.6 - Prob. 59SCh. 2.6 - Prob. 60SCh. 2.6 - Prob. 61SCh. 2.6 - Prob. 62SCh. 2.6 - Prob. 63SCh. 2.6 - Prob. 64SCh. 2.6 - Prob. 65SCh. 2.6 - Prob. 66SCh. 2.6 - Prob. 67SCh. 2.6 - Prob. 68SCh. 2.6 - Prob. 69SCh. 2.6 - Prob. 70SCh. 2.6 - Prob. 71SCh. 2.6 - Prob. 72SCh. 2.6 - Prob. 73SCh. 2.6 - Prob. 74SCh. 2.6 - Prob. 75SCh. 2.6 - Prob. 76SCh. 2.6 - Prob. 77SCh. 2.6 - Prob. 78ACh. 2.6 - Prob. 79ACh. 2.6 - Prob. 80ACh. 2.6 - Prob. 81ACh. 2.6 - Prob. 82ACh. 2.6 - Prob. 83PCh. 2.6 - Prob. 84PCh. 2.6 - Prob. 85PCh. 2.6 - Prob. 86PCh. 2.6 - Prob. 87PCh. 2.6 - Prob. 88PCh. 2.6 - Prob. 89PCh. 2.6 - Prob. 90PCh. 2.6 - Prob. 91PCh. 2.6 - Prob. 92PCh. 2.6 - Prob. 93PCh. 2.6 - Prob. 94PCh. 2.6 - Prob. 95PCh. 2.6 - Prob. 96PCh. 2.6 - Prob. 97PCh. 2.6 - Prob. 98PCh. 2.6 - Prob. 99PCh. 2.6 - Prob. 1TFCh. 2.6 - Prob. 2TFCh. 2.6 - Prob. 3TFCh. 2 - Prob. 1DCh. 2 - Prob. 2DCh. 2 - Prob. 3DCh. 2 - Prob. 4DCh. 2 - Prob. 5DCh. 2 - Prob. 6DCh. 2 - Prob. 7DCh. 2 - Prob. 8DCh. 2 - Prob. 9DCh. 2 - Prob. 10DCh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Prob. 1NDRCh. 2 - Prob. 2NDRCh. 2 - Prob. 3NDRCh. 2 - Prob. 4NDRCh. 2 - Prob. 5NDRCh. 2 - Prob. 6NDRCh. 2 - Prob. 7NDRCh. 2 - Prob. 8NDRCh. 2 - Prob. 9NDRCh. 2 - Prob. 10NDRCh. 2 - Prob. 11NDRCh. 2 - Prob. 12NDRCh. 2 - Prob. 13NDRCh. 2 - Prob. 14NDRCh. 2 - Prob. 15NDRCh. 2 - Prob. 16NDRCh. 2 - Prob. 17NDRCh. 2 - Prob. 18NDRCh. 2 - Prob. 19NDRCh. 2 - Prob. 20NDRCh. 2 - Prob. 21NDRCh. 2 - Prob. 22NDRCh. 2 - Prob. 23NDRCh. 2 - Prob. 24NDRCh. 2 - Prob. 25NDRCh. 2 - Prob. 26NDRCh. 2 - Prob. 27NDRCh. 2 - Prob. 28NDRCh. 2 - Prob. 29NDRCh. 2 - Prob. 30NDRCh. 2 - Prob. 31NDRCh. 2 - Prob. 32NDRCh. 2 - Prob. 33NDRCh. 2 - Prob. 34NDRCh. 2 - Prob. 35NDRCh. 2 - Prob. 36NDRCh. 2 - Prob. 37NDRCh. 2 - Prob. 38NDRCh. 2 - Prob. 39NDRCh. 2 - Prob. 40NDRCh. 2 - Prob. 41NDRCh. 2 - Prob. 42NDRCh. 2 - Prob. 43NDRCh. 2 - Prob. 44NDRCh. 2 - Prob. 45NDRCh. 2 - Prob. 1SCCh. 2 - Prob. 2SCCh. 2 - Prob. 3SCCh. 2 - Prob. 4SCCh. 2 - Prob. 5SCCh. 2 - Prob. 6SCCh. 2 - Prob. 7SCCh. 2 - Prob. 8SCCh. 2 - Prob. 9SCCh. 2 - Prob. 10SCCh. 2 - Prob. 11SCCh. 2 - Prob. 12SCCh. 2 - Prob. 13SCCh. 2 - Prob. 14SCCh. 2 - Prob. 15SCCh. 2 - Prob. 16SCCh. 2 - Prob. 17SCCh. 2 - Prob. 18SCCh. 2 - Prob. 19SCCh. 2 - Prob. 20SCCh. 2 - Prob. 21SCCh. 2 - Prob. 22SCCh. 2 - Prob. 23SCCh. 2 - Prob. 24SCCh. 2 - Prob. 25SCCh. 2 - Prob. 26SCCh. 2 - Prob. 27SCCh. 2 - Prob. 28SCCh. 2 - Prob. 29SCCh. 2 - Prob. 30SCCh. 2 - Prob. 31SCCh. 2 - Prob. 32SCCh. 2 - Prob. 33SCCh. 2 - Prob. 34SCCh. 2 - Prob. 35SCCh. 2 - Prob. 36SCCh. 2 - Prob. 37SCCh. 2 - Prob. 38SCCh. 2 - Prob. 39SCCh. 2 - Prob. 40SCCh. 2 - Prob. 41SCCh. 2 - Prob. 42SCCh. 2 - Prob. ACPCh. 2 - Prob. BCPCh. 2 - Prob. CCPCh. 2 - Prob. DCP
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- Provethat a) prove that for any irrational numbers there exists? asequence of rational numbers Xn converg to S. b) let S: RR be a sunctions-t. f(x)=(x-1) arc tan (x), xe Q 3(x-1) 1+x² x&Q Show that lim f(x)= 0 14x C) For any set A define the set -A=yarrow_forwardQ2: Find the interval and radius of convergence for the following series: Σ n=1 (-1)η-1 xn narrow_forward8. Evaluate arctan x dx a) xartanx 2 2 In(1 + x²) + C b) xartanx + 1½-3ln(1 + x²) + C c) xartanx + In(1 + x²) + C d) (arctanx)² + C 2 9) Evaluate Inx³ dx 3 a) +C b) ln x² + C c)¾½ (lnx)² d) 3x(lnx − 1) + C - x 10) Determine which integral is obtained when the substitution x = So¹² √1 - x²dx sine is made in the integral πT π π a) √ sin cos e de b) √ cos² de c) c Ꮎ Ꮎ cos² 0 de c) cos e de d) for cos² e de πT 11. Evaluate tan³xdx 1 a) b) c) [1 - In 2] 2 2 c) [1 − In2] d)½½[1+ In 2]arrow_forward
- 12. Evaluate ſ √9-x2 -dx. x2 a) C 9-x2 √9-x2 - x2 b) C - x x arcsin ½-½ c) C + √9 - x² + arcsin x d) C + √9-x2 x2 13. Find the indefinite integral S cos³30 √sin 30 dᎾ . 2√√sin 30 (5+sin²30) √sin 30 (3+sin²30) a) C+ √sin 30(5-sin²30) b) C + c) C + 5 5 5 10 d) C + 2√√sin 30 (3-sin²30) 2√√sin 30 (5-sin²30) e) C + 5 15 14. Find the indefinite integral ( sin³ 4xcos 44xdx. a) C+ (7-5cos24x)cos54x b) C (7-5cos24x)cos54x (7-5cos24x)cos54x - 140 c) C - 120 140 d) C+ (7-5cos24x)cos54x e) C (7-5cos24x)cos54x 4 4 15. Find the indefinite integral S 2x2 dx. ex - a) C+ (x²+2x+2)ex b) C (x² + 2x + 2)e-* d) C2(x²+2x+2)e¯* e) C + 2(x² + 2x + 2)e¯* - c) C2x(x²+2x+2)e¯*arrow_forward4. Which substitution would you use to simplify the following integrand? S a) x = sin b) x = 2 tan 0 c) x = 2 sec 3√√3 3 x3 5. After making the substitution x = = tan 0, the definite integral 2 2 3 a) ៖ ស្លឺ sin s π - dᎾ 16 0 cos20 b) 2/4 10 cos 20 π sin30 6 - dᎾ c) Π 1 cos³0 3 · de 16 0 sin20 1 x²√x²+4 3 (4x²+9)2 π d) cos²8 16 0 sin³0 dx d) x = tan 0 dx simplifies to: de 6. In order to evaluate (tan 5xsec7xdx, which would be the most appropriate strategy? a) Separate a sec²x factor b) Separate a tan²x factor c) Separate a tan xsecx factor 7. Evaluate 3x x+4 - dx 1 a) 3x+41nx + 4 + C b) 31n|x + 4 + C c) 3 ln x + 4+ C d) 3x - 12 In|x + 4| + C x+4arrow_forward1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps (each step must be justified). Theorem 0.1 (Abel's Theorem). If y1 and y2 are solutions of the differential equation y" + p(t) y′ + q(t) y = 0, where p and q are continuous on an open interval, then the Wronskian is given by W (¥1, v2)(t) = c exp(− [p(t) dt), where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or W (y1, y2)(t) = 0 for every t in I. 1. (a) From the two equations (which follow from the hypotheses), show that y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0, 2. (b) Observe that Hence, conclude that (YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0. W'(y1, y2)(t) = yY2 - Y1 y2- W' + p(t) W = 0. 3. (c) Use the result from the previous step to complete the proof of the theorem.arrow_forward
- 2. Observations on the Wronskian. Suppose the functions y₁ and y2 are solutions to the differential equation p(x)y" + q(x)y' + r(x) y = 0 on an open interval I. 1. (a) Prove that if y₁ and y2 both vanish at the same point in I, then y₁ and y2 cannot form a fundamental set of solutions. 2. (b) Prove that if y₁ and y2 both attain a maximum or minimum at the same point in I, then y₁ and Y2 cannot form a fundamental set of solutions. 3. (c) show that the functions & and t² are linearly independent on the interval (−1, 1). Verify that both are solutions to the differential equation t² y″ – 2ty' + 2y = 0. Then justify why this does not contradict Abel's theorem. 4. (d) What can you conclude about the possibility that t and t² are solutions to the differential equation y" + q(x) y′ + r(x)y = 0?arrow_forwardQuestion 4 Find an equation of (a) The plane through the point (2, 0, 1) and perpendicular to the line x = y=2-t, z=3+4t. 3t, (b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y. (c) The plane that contains the line x = 1+t, y = 2 − t, z = 4 - 3t and is parallel to the plane 5x + 2y + z = 1. (d) The plane that passes through the point (1,2,3) and contains the line x = 3t, y = 1+t, and z = 2-t. (e) The plane that contains the lines L₁: x = 1 + t, y = 1 − t, z = 2t and L2 : x = 2 − s, y = s, z = 2.arrow_forwardPlease find all values of x.arrow_forward
- 3. Consider the initial value problem 9y" +12y' + 4y = 0, y(0) = a>0: y′(0) = −1. Solve the problem and find the value of a such that the solution of the initial value problem is always positive.arrow_forward5. Euler's equation. Determine the values of a for which all solutions of the equation 5 x²y" + axy' + y = 0 that have the form (A + B log x) x* or Ax¹¹ + Bä” tend to zero as a approaches 0.arrow_forward4. Problem on variable change. The purpose of this problem is to perform an appropriate change of variables in order to reduce the problem to a second-order equation with constant coefficients. ty" + (t² − 1)y'′ + t³y = 0, 0arrow_forward
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