Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Chapter 1.4, Problem 1TB
To determine
The roots of piece-wise defined functions.
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Students have asked these similar questions
00
(a) Starting with the geometric series Σ X^, find the sum of the series
n = 0
00
Σηχη - 1,
|x| < 1.
n = 1
(b) Find the sum of each of the following series.
00
Σnx",
n = 1
|x| < 1
(ii)
n = 1
sin
(c) Find the sum of each of the following series.
(i)
00
Σn(n-1)x^, |x| <1
n = 2
(ii)
00
n = 2
n²
- n
4n
(iii)
M8
n = 1
շո
(a) Use differentiation to find a power series representation for
1
f(x)
=
(4 + x)²*
f(x)
=
00
Σ
n = 0
What is the radius of convergence, R?
R =
(b) Use part (a) to find a power series for
f(x)
=
1
(4 + x)³°
f(x) =
00
Σ
n = 0
What is the radius of convergence, R?
R =
(c) Use part (b) to find a power series for
f(x)
=
x²
(4 + x)³*
00
f(x) = Σ
n = 2
What is the radius of convergence, R?
R =
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Chapter 1 Solutions
Calculus
Ch. 1.1 - Prob. 1TBCh. 1.1 - Prob. 2TBCh. 1.1 - Prob. 0CCh. 1.1 - Prob. 1CCh. 1.1 - Prob. 2CCh. 1.1 - Prob. 3CCh. 1.1 - Prob. 4CCh. 1.1 - Prob. 5CCh. 1.1 - Prob. 6CCh. 1.1 - Prob. 7C
Ch. 1.1 - Prob. 8CCh. 1.1 - Prob. 9CCh. 1.1 - Prob. 10CCh. 1.1 - Prob. 11CCh. 1.1 - Prob. 12CCh. 1.1 - Prob. 13CCh. 1.1 - Prob. 14CCh. 1.1 - Prob. 15CCh. 1.1 - Prob. 16CCh. 1.1 - Prob. 17CCh. 1.1 - Prob. 18CCh. 1.1 - Prob. 19CCh. 1.1 - Prob. 20CCh. 1.1 - Prob. 21SCh. 1.1 - Prob. 22SCh. 1.1 - Prob. 23SCh. 1.1 - Prob. 24SCh. 1.1 - Prob. 25SCh. 1.1 - Prob. 26SCh. 1.1 - Prob. 27SCh. 1.1 - Prob. 28SCh. 1.1 - Prob. 29SCh. 1.1 - Prob. 30SCh. 1.1 - Prob. 31SCh. 1.1 - Prob. 32SCh. 1.1 - Prob. 33SCh. 1.1 - Prob. 34SCh. 1.1 - Prob. 35SCh. 1.1 - Prob. 36SCh. 1.1 - Prob. 37SCh. 1.1 - Prob. 38SCh. 1.1 - Prob. 39SCh. 1.1 - Prob. 40SCh. 1.1 - Prob. 41SCh. 1.1 - Prob. 42SCh. 1.1 - Prob. 43SCh. 1.1 - Prob. 44SCh. 1.1 - Prob. 45SCh. 1.1 - Prob. 46SCh. 1.1 - Prob. 47SCh. 1.1 - Prob. 48SCh. 1.1 - Prob. 49SCh. 1.1 - Prob. 50SCh. 1.1 - Prob. 51SCh. 1.1 - Prob. 52SCh. 1.1 - Prob. 53SCh. 1.1 - Prob. 54SCh. 1.1 - Prob. 55SCh. 1.1 - Prob. 56SCh. 1.1 - Prob. 57SCh. 1.1 - Prob. 58SCh. 1.1 - Prob. 59SCh. 1.1 - Prob. 60SCh. 1.1 - Prob. 61SCh. 1.1 - Prob. 62SCh. 1.1 - Prob. 63SCh. 1.1 - Prob. 64SCh. 1.1 - Prob. 65SCh. 1.1 - Prob. 66SCh. 1.1 - Prob. 67SCh. 1.1 - Prob. 68SCh. 1.1 - Prob. 69SCh. 1.1 - Prob. 70SCh. 1.1 - Prob. 71SCh. 1.1 - Prob. 72SCh. 1.1 - Prob. 73SCh. 1.1 - Prob. 74SCh. 1.1 - Prob. 75ACh. 1.1 - Prob. 76ACh. 1.1 - Prob. 77ACh. 1.1 - Prob. 78PCh. 1.1 - Prob. 79PCh. 1.1 - Prob. 80PCh. 1.1 - Prob. 81PCh. 1.1 - Prob. 1TFCh. 1.1 - Prob. 2TFCh. 1.2 - Prob. 1TBCh. 1.2 - Prob. 2TBCh. 1.2 - Prob. 0CCh. 1.2 - Prob. 1CCh. 1.2 - Prob. 2CCh. 1.2 - Prob. 3CCh. 1.2 - Prob. 4CCh. 1.2 - Prob. 5CCh. 1.2 - Prob. 6CCh. 1.2 - Prob. 7CCh. 1.2 - Prob. 8CCh. 1.2 - Prob. 9CCh. 1.2 - Prob. 10CCh. 1.2 - Prob. 11CCh. 1.2 - Prob. 12CCh. 1.2 - Prob. 13CCh. 1.2 - Prob. 14CCh. 1.2 - Prob. 15CCh. 1.2 - Prob. 16CCh. 1.2 - Prob. 17CCh. 1.2 - Prob. 18CCh. 1.2 - Prob. 19SCh. 1.2 - Prob. 20SCh. 1.2 - Prob. 21SCh. 1.2 - Prob. 22SCh. 1.2 - Prob. 23SCh. 1.2 - Prob. 24SCh. 1.2 - Prob. 25SCh. 1.2 - Prob. 26SCh. 1.2 - Prob. 27SCh. 1.2 - Prob. 28SCh. 1.2 - Prob. 29SCh. 1.2 - Prob. 30SCh. 1.2 - Prob. 31SCh. 1.2 - Prob. 32SCh. 1.2 - Prob. 33SCh. 1.2 - Prob. 34SCh. 1.2 - Prob. 35SCh. 1.2 - Prob. 36SCh. 1.2 - Prob. 37SCh. 1.2 - Prob. 38SCh. 1.2 - Prob. 39SCh. 1.2 - Prob. 40SCh. 1.2 - Prob. 41SCh. 1.2 - Prob. 42SCh. 1.2 - Prob. 43SCh. 1.2 - Prob. 44SCh. 1.2 - Prob. 45SCh. 1.2 - Prob. 46SCh. 1.2 - Prob. 47SCh. 1.2 - Prob. 48SCh. 1.2 - Prob. 49SCh. 1.2 - Prob. 50SCh. 1.2 - Prob. 51SCh. 1.2 - Prob. 52SCh. 1.2 - Prob. 53SCh. 1.2 - Prob. 54SCh. 1.2 - Prob. 55SCh. 1.2 - Prob. 56SCh. 1.2 - Prob. 57SCh. 1.2 - Prob. 58SCh. 1.2 - Prob. 59SCh. 1.2 - Prob. 60SCh. 1.2 - Prob. 61SCh. 1.2 - Prob. 62SCh. 1.2 - Prob. 63SCh. 1.2 - Prob. 64SCh. 1.2 - Prob. 65ACh. 1.2 - Prob. 66ACh. 1.2 - Prob. 67ACh. 1.2 - Prob. 68PCh. 1.2 - Prob. 69PCh. 1.2 - Prob. 70PCh. 1.2 - Prob. 71PCh. 1.2 - Prob. 1TFCh. 1.2 - Prob. 2TFCh. 1.3 - Prob. 1TBCh. 1.3 - Prob. 2TBCh. 1.3 - Prob. 0CCh. 1.3 - Prob. 1CCh. 1.3 - Prob. 2CCh. 1.3 - Prob. 3CCh. 1.3 - Prob. 4CCh. 1.3 - Prob. 5CCh. 1.3 - Prob. 6CCh. 1.3 - Prob. 7CCh. 1.3 - Prob. 8CCh. 1.3 - Prob. 9CCh. 1.3 - Prob. 10CCh. 1.3 - Prob. 11CCh. 1.3 - Prob. 12CCh. 1.3 - Prob. 13CCh. 1.3 - Prob. 14CCh. 1.3 - Prob. 15CCh. 1.3 - Prob. 16CCh. 1.3 - Prob. 17CCh. 1.3 - Prob. 18CCh. 1.3 - Prob. 19CCh. 1.3 - Prob. 20CCh. 1.3 - Prob. 21CCh. 1.3 - Prob. 22CCh. 1.3 - Prob. 23SCh. 1.3 - Prob. 24SCh. 1.3 - Prob. 25SCh. 1.3 - Prob. 26SCh. 1.3 - Prob. 27SCh. 1.3 - Prob. 28SCh. 1.3 - Prob. 29SCh. 1.3 - Prob. 30SCh. 1.3 - Prob. 31SCh. 1.3 - Prob. 32SCh. 1.3 - Prob. 33SCh. 1.3 - Prob. 34SCh. 1.3 - Prob. 35SCh. 1.3 - Prob. 36SCh. 1.3 - Prob. 37SCh. 1.3 - Prob. 38SCh. 1.3 - Prob. 39SCh. 1.3 - Prob. 40SCh. 1.3 - Prob. 41SCh. 1.3 - Prob. 42SCh. 1.3 - Prob. 43SCh. 1.3 - Prob. 44SCh. 1.3 - Prob. 45ACh. 1.3 - Prob. 46ACh. 1.3 - Prob. 47PCh. 1.3 - Prob. 48PCh. 1.3 - Prob. 49PCh. 1.3 - Prob. 50PCh. 1.3 - Prob. 51PCh. 1.3 - Prob. 52PCh. 1.3 - Prob. 53PCh. 1.3 - Prob. 54PCh. 1.3 - Prob. 55PCh. 1.3 - Prob. 56PCh. 1.3 - Prob. 57PCh. 1.3 - Prob. 58PCh. 1.3 - Prob. 59PCh. 1.3 - Prob. 60PCh. 1.3 - Prob. 61PCh. 1.3 - Prob. 62PCh. 1.3 - Prob. 63PCh. 1.3 - Prob. 64PCh. 1.3 - Prob. 65PCh. 1.3 - Prob. 66PCh. 1.3 - Prob. 67PCh. 1.3 - Prob. 68PCh. 1.3 - Prob. 69PCh. 1.3 - Prob. 70PCh. 1.3 - Prob. 71PCh. 1.3 - Prob. 72PCh. 1.3 - Prob. 1TFCh. 1.3 - Prob. 2TFCh. 1.3 - Prob. 3TFCh. 1.3 - Prob. 4TFCh. 1.4 - Prob. 1TBCh. 1.4 - Prob. 2TBCh. 1.4 - Prob. 0CCh. 1.4 - Prob. 1CCh. 1.4 - Prob. 2CCh. 1.4 - Prob. 3CCh. 1.4 - Prob. 4CCh. 1.4 - Prob. 5CCh. 1.4 - Prob. 6CCh. 1.4 - Prob. 7CCh. 1.4 - Prob. 8CCh. 1.4 - Prob. 9CCh. 1.4 - Prob. 10CCh. 1.4 - Prob. 11CCh. 1.4 - Prob. 12CCh. 1.4 - Prob. 13CCh. 1.4 - Prob. 14CCh. 1.4 - Prob. 15CCh. 1.4 - Prob. 16CCh. 1.4 - Prob. 17CCh. 1.4 - Prob. 18CCh. 1.4 - Prob. 19CCh. 1.4 - Prob. 20CCh. 1.4 - Prob. 21CCh. 1.4 - Prob. 22CCh. 1.4 - Prob. 23SCh. 1.4 - Prob. 24SCh. 1.4 - Prob. 25SCh. 1.4 - Prob. 26SCh. 1.4 - Prob. 27SCh. 1.4 - Prob. 28SCh. 1.4 - Prob. 29SCh. 1.4 - Prob. 30SCh. 1.4 - Prob. 31SCh. 1.4 - Prob. 32SCh. 1.4 - Prob. 33SCh. 1.4 - Prob. 34SCh. 1.4 - Prob. 35SCh. 1.4 - Prob. 36SCh. 1.4 - Prob. 37SCh. 1.4 - Prob. 38SCh. 1.4 - Prob. 39SCh. 1.4 - Prob. 40SCh. 1.4 - Prob. 41SCh. 1.4 - Prob. 42SCh. 1.4 - Prob. 43SCh. 1.4 - Prob. 44SCh. 1.4 - Prob. 45SCh. 1.4 - Prob. 46SCh. 1.4 - Prob. 47SCh. 1.4 - Prob. 48SCh. 1.4 - Prob. 49SCh. 1.4 - Prob. 50SCh. 1.4 - Prob. 51SCh. 1.4 - Prob. 52SCh. 1.4 - Prob. 53SCh. 1.4 - Prob. 54SCh. 1.4 - Prob. 55SCh. 1.4 - Prob. 56SCh. 1.4 - Prob. 57SCh. 1.4 - Prob. 58SCh. 1.4 - Prob. 59SCh. 1.4 - Prob. 60SCh. 1.4 - Prob. 61SCh. 1.4 - Prob. 62SCh. 1.4 - Prob. 63SCh. 1.4 - Prob. 64SCh. 1.4 - Prob. 65SCh. 1.4 - Prob. 66SCh. 1.4 - Prob. 67SCh. 1.4 - Prob. 68SCh. 1.4 - Prob. 69SCh. 1.4 - Prob. 70SCh. 1.4 - Prob. 71SCh. 1.4 - Prob. 72SCh. 1.4 - Prob. 73SCh. 1.4 - Prob. 74SCh. 1.4 - Prob. 75ACh. 1.4 - Prob. 76ACh. 1.4 - Prob. 77ACh. 1.4 - Prob. 78ACh. 1.4 - Prob. 79ACh. 1.4 - Prob. 80ACh. 1.4 - Prob. 81PCh. 1.4 - Prob. 82PCh. 1.4 - Prob. 83PCh. 1.4 - Prob. 84PCh. 1.4 - Prob. 85PCh. 1.4 - Prob. 86PCh. 1.4 - Prob. 87PCh. 1.4 - Prob. 88PCh. 1.4 - Prob. 89PCh. 1.4 - Prob. 90PCh. 1.4 - Prob. 91PCh. 1.4 - Prob. 92PCh. 1.4 - Prob. 93PCh. 1.4 - Prob. 1TFCh. 1.4 - Prob. 2TFCh. 1.4 - Prob. 3TFCh. 1.4 - Prob. 4TFCh. 1.4 - Prob. 5TFCh. 1.5 - Prob. 1TBCh. 1.5 - Prob. 2TBCh. 1.5 - Prob. 0CCh. 1.5 - Prob. 1CCh. 1.5 - Prob. 2CCh. 1.5 - Prob. 3CCh. 1.5 - Prob. 4CCh. 1.5 - Prob. 5CCh. 1.5 - Prob. 6CCh. 1.5 - Prob. 7CCh. 1.5 - Prob. 8CCh. 1.5 - Prob. 9CCh. 1.5 - Prob. 10CCh. 1.5 - Prob. 11CCh. 1.5 - Prob. 12CCh. 1.5 - Prob. 13CCh. 1.5 - Prob. 14CCh. 1.5 - Prob. 15CCh. 1.5 - Prob. 16CCh. 1.5 - Prob. 17CCh. 1.5 - Prob. 18CCh. 1.5 - Prob. 19CCh. 1.5 - Prob. 20CCh. 1.5 - Prob. 21CCh. 1.5 - Prob. 22CCh. 1.5 - Prob. 23CCh. 1.5 - Prob. 24CCh. 1.5 - Prob. 25SCh. 1.5 - Prob. 26SCh. 1.5 - Prob. 27SCh. 1.5 - Prob. 28SCh. 1.5 - Prob. 29SCh. 1.5 - Prob. 30SCh. 1.5 - Prob. 31SCh. 1.5 - Prob. 32SCh. 1.5 - Prob. 33SCh. 1.5 - Prob. 34SCh. 1.5 - Prob. 35SCh. 1.5 - Prob. 36SCh. 1.5 - Prob. 37SCh. 1.5 - Prob. 38SCh. 1.5 - Prob. 39SCh. 1.5 - Prob. 40SCh. 1.5 - Prob. 41SCh. 1.5 - Prob. 42SCh. 1.5 - Prob. 43SCh. 1.5 - Prob. 44SCh. 1.5 - Prob. 45SCh. 1.5 - Prob. 46SCh. 1.5 - Prob. 47SCh. 1.5 - Prob. 48SCh. 1.5 - Prob. 49SCh. 1.5 - Prob. 50SCh. 1.5 - Prob. 51SCh. 1.5 - Prob. 52SCh. 1.5 - Prob. 53SCh. 1.5 - Prob. 54SCh. 1.5 - Prob. 55SCh. 1.5 - Prob. 56SCh. 1.5 - Prob. 57SCh. 1.5 - Prob. 58SCh. 1.5 - Prob. 59SCh. 1.5 - Prob. 60SCh. 1.5 - Prob. 61SCh. 1.5 - Prob. 62SCh. 1.5 - Prob. 63SCh. 1.5 - Prob. 64SCh. 1.5 - Prob. 65SCh. 1.5 - Prob. 66SCh. 1.5 - Prob. 67SCh. 1.5 - Prob. 68SCh. 1.5 - Prob. 69SCh. 1.5 - Prob. 70SCh. 1.5 - Prob. 71SCh. 1.5 - Prob. 72SCh. 1.5 - Prob. 73SCh. 1.5 - Prob. 74SCh. 1.5 - Prob. 75SCh. 1.5 - Prob. 76SCh. 1.5 - Prob. 77SCh. 1.5 - Prob. 78SCh. 1.5 - Prob. 79SCh. 1.5 - Prob. 80SCh. 1.5 - Prob. 81SCh. 1.5 - Prob. 82SCh. 1.5 - Prob. 83SCh. 1.5 - Prob. 84SCh. 1.5 - Prob. 85SCh. 1.5 - Prob. 86SCh. 1.5 - Prob. 87ACh. 1.5 - Prob. 88ACh. 1.5 - Prob. 89PCh. 1.5 - Prob. 90PCh. 1.5 - Prob. 91PCh. 1.5 - Prob. 92PCh. 1.5 - Prob. 93PCh. 1.5 - Prob. 94PCh. 1.5 - Prob. 95PCh. 1.5 - Prob. 96PCh. 1.5 - Prob. 97PCh. 1.5 - Prob. 98PCh. 1.5 - Prob. 99PCh. 1.5 - Prob. 100PCh. 1.5 - Prob. 1TFCh. 1.5 - Prob. 2TFCh. 1.5 - Prob. 3TFCh. 1.5 - Prob. 4TFCh. 1.5 - Prob. 5TFCh. 1.5 - Prob. 6TFCh. 1.5 - Prob. 7TFCh. 1.6 - Prob. 1TBCh. 1.6 - Prob. 2TBCh. 1.6 - Prob. 0CCh. 1.6 - Prob. 1CCh. 1.6 - Prob. 2CCh. 1.6 - Prob. 3CCh. 1.6 - Prob. 4CCh. 1.6 - Prob. 5CCh. 1.6 - Prob. 6CCh. 1.6 - Prob. 7CCh. 1.6 - Prob. 8CCh. 1.6 - Prob. 9CCh. 1.6 - Prob. 10CCh. 1.6 - Prob. 11CCh. 1.6 - Prob. 12CCh. 1.6 - Prob. 13CCh. 1.6 - Prob. 14CCh. 1.6 - Prob. 15CCh. 1.6 - Prob. 16CCh. 1.6 - Prob. 17CCh. 1.6 - Prob. 18CCh. 1.6 - Prob. 19CCh. 1.6 - Prob. 20CCh. 1.6 - Prob. 21CCh. 1.6 - Prob. 22CCh. 1.6 - Prob. 23SCh. 1.6 - Prob. 24SCh. 1.6 - Prob. 25SCh. 1.6 - Prob. 26SCh. 1.6 - Prob. 27SCh. 1.6 - Prob. 28SCh. 1.6 - Prob. 29SCh. 1.6 - Prob. 30SCh. 1.6 - Prob. 31SCh. 1.6 - Prob. 32SCh. 1.6 - Prob. 33SCh. 1.6 - Prob. 34SCh. 1.6 - Prob. 35SCh. 1.6 - Prob. 36SCh. 1.6 - Prob. 37SCh. 1.6 - Prob. 38SCh. 1.6 - Prob. 39SCh. 1.6 - Prob. 40SCh. 1.6 - Prob. 41SCh. 1.6 - Prob. 42SCh. 1.6 - Prob. 43SCh. 1.6 - Prob. 44SCh. 1.6 - Prob. 45SCh. 1.6 - Prob. 46SCh. 1.6 - Prob. 47SCh. 1.6 - Prob. 48SCh. 1.6 - Prob. 49SCh. 1.6 - Prob. 50SCh. 1.6 - Prob. 51SCh. 1.6 - Prob. 52SCh. 1.6 - Prob. 53SCh. 1.6 - Prob. 54SCh. 1.6 - Prob. 55SCh. 1.6 - Prob. 56SCh. 1.6 - Prob. 57SCh. 1.6 - Prob. 58SCh. 1.6 - Prob. 59SCh. 1.6 - Prob. 60SCh. 1.6 - Prob. 61SCh. 1.6 - Prob. 62SCh. 1.6 - Prob. 63SCh. 1.6 - Prob. 64SCh. 1.6 - Prob. 65SCh. 1.6 - Prob. 66SCh. 1.6 - Prob. 67SCh. 1.6 - Prob. 68SCh. 1.6 - Prob. 69SCh. 1.6 - Prob. 70SCh. 1.6 - Prob. 71SCh. 1.6 - Prob. 72SCh. 1.6 - Prob. 73SCh. 1.6 - Prob. 74SCh. 1.6 - Prob. 75SCh. 1.6 - Prob. 76SCh. 1.6 - Prob. 77SCh. 1.6 - Prob. 78SCh. 1.6 - Prob. 79SCh. 1.6 - Prob. 80SCh. 1.6 - Prob. 81ACh. 1.6 - Prob. 82ACh. 1.6 - Prob. 83ACh. 1.6 - Prob. 84ACh. 1.6 - Prob. 85PCh. 1.6 - Prob. 86PCh. 1.6 - Prob. 87PCh. 1.6 - Prob. 88PCh. 1.6 - Prob. 89PCh. 1.6 - Prob. 90PCh. 1.6 - Prob. 91PCh. 1.6 - Prob. 92PCh. 1.6 - Prob. 93PCh. 1.6 - Prob. 94PCh. 1.6 - Prob. 1TFCh. 1.6 - Prob. 2TFCh. 1.6 - Prob. 3TFCh. 1.6 - Prob. 4TFCh. 1.6 - Prob. 5TFCh. 1.6 - Prob. 6TFCh. 1.6 - Prob. 7TFCh. 1 - Prob. 1DCh. 1 - Prob. 2DCh. 1 - Prob. 3DCh. 1 - Prob. 4DCh. 1 - Prob. 5DCh. 1 - Prob. 6DCh. 1 - Prob. 7DCh. 1 - Prob. 8DCh. 1 - Prob. 9DCh. 1 - Prob. 10DCh. 1 - Prob. 1TCh. 1 - Prob. 2TCh. 1 - Prob. 3TCh. 1 - Prob. 4TCh. 1 - Prob. 5TCh. 1 - Prob. 6TCh. 1 - Prob. 7TCh. 1 - Prob. 8TCh. 1 - Prob. 9TCh. 1 - Prob. 10TCh. 1 - Prob. 11TCh. 1 - Prob. 12TCh. 1 - Prob. 13TCh. 1 - Prob. 14TCh. 1 - Prob. 1LRIFCh. 1 - Prob. 2LRIFCh. 1 - Prob. 3LRIFCh. 1 - Prob. 4LRIFCh. 1 - Prob. 5LRIFCh. 1 - Prob. 6LRIFCh. 1 - Prob. 7LRIFCh. 1 - Prob. 8LRIFCh. 1 - Prob. 9LRIFCh. 1 - Prob. 10LRIFCh. 1 - Prob. 11LRIFCh. 1 - Prob. 12LRIFCh. 1 - Prob. 13LRIFCh. 1 - Prob. 14LRIFCh. 1 - Prob. 15LRIFCh. 1 - Prob. 16LRIFCh. 1 - Prob. 17LRIFCh. 1 - Prob. 18LRIFCh. 1 - Prob. 19LRIFCh. 1 - Prob. 20LRIFCh. 1 - Prob. 21LRIFCh. 1 - Prob. 22LRIFCh. 1 - Prob. 23LRIFCh. 1 - Prob. 24LRIFCh. 1 - Prob. 25LRIFCh. 1 - Prob. 26LRIFCh. 1 - Prob. 27LRIFCh. 1 - Prob. 28LRIFCh. 1 - Prob. 29LRIFCh. 1 - Prob. 30LRIFCh. 1 - Prob. 31LRIFCh. 1 - Prob. 32LRIFCh. 1 - Prob. 33LRIFCh. 1 - Prob. 34LRIFCh. 1 - Prob. 35LRIFCh. 1 - Prob. 36LRIFCh. 1 - Prob. 37LRIFCh. 1 - Prob. 38LRIFCh. 1 - Prob. 39LRIFCh. 1 - Prob. 40LRIFCh. 1 - Prob. 41LRIFCh. 1 - Prob. 42LRIFCh. 1 - Prob. 43LRIFCh. 1 - Prob. 44LRIFCh. 1 - Prob. 45LRIFCh. 1 - Prob. 46LRIFCh. 1 - Prob. 47LRIFCh. 1 - Prob. 48LRIFCh. 1 - Prob. 49LRIFCh. 1 - Prob. 50LRIFCh. 1 - Prob. 1SCCh. 1 - Prob. 2SCCh. 1 - Prob. 3SCCh. 1 - Prob. 4SCCh. 1 - Prob. 5SCCh. 1 - Prob. 6SCCh. 1 - Prob. 7SCCh. 1 - Prob. 8SCCh. 1 - Prob. 9SCCh. 1 - Prob. 10SCCh. 1 - Prob. 11SCCh. 1 - Prob. 12SCCh. 1 - Prob. 13SCCh. 1 - Prob. 14SCCh. 1 - Prob. 15SCCh. 1 - Prob. 16SCCh. 1 - Prob. 17SCCh. 1 - Prob. 18SCCh. 1 - Prob. 19SCCh. 1 - Prob. 20SCCh. 1 - Prob. 21SCCh. 1 - Prob. 22SCCh. 1 - Prob. 23SCCh. 1 - Prob. 24SCCh. 1 - Prob. 25SCCh. 1 - Prob. 26SCCh. 1 - Prob. 27SCCh. 1 - Prob. 28SCCh. 1 - Prob. 29SCCh. 1 - Prob. 30SCCh. 1 - Prob. 31SCCh. 1 - Prob. 32SCCh. 1 - Prob. ACPCh. 1 - Prob. BCPCh. 1 - Prob. CCPCh. 1 - Prob. DCP
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- Find the volume of the solid that lies under the paraboloid z = 81 - x² - y² and within the cylinder (x − 1)² + y² = 1. A plot of an example of a similar solid is shown below. (Answer accurate to 2 decimal places). Volume using Double Integral Paraboloid & Cylinder -3 Hint: The integral and region is defined in polar coordinates.arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √4(1–2² 4(1 - x² - y²) dA R 3 R = {(r,0) | 0 ≤ r≤ 2,0π ≤0≤¼˜}. Hint: The integral is defined in rectangular coordinates. The Region is defined in polar coordinates.arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). R - 1 · {(r,0) | 1 ≤ r≤ 5,½π≤ 0<1π}. Hint: Be sure to convert to Polar coordinates. Use the correct differential for Polar Coordinates.arrow_forward
- Evaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √ √2(x+y) dA R R = {(x, y) | 4 < x² + y² < 25,0 < x} Hint: The integral and Region is defined in rectangular coordinates.arrow_forwardHW: The frame shown in the figure is pinned at A and C. Use moment distribution method, with and without modifications, to draw NFD, SFD, and BMD. B I I 40 kN/m A 3 m 4 marrow_forwardLet the region R be the area enclosed by the function f(x)= = 3x² and g(x) = 4x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth. y 11 10 9 00 8 7 9 5 4 3 2 1 -1 -1 x 1 2arrow_forward
- Let the region R be the area enclosed by the function f(x) = ex — 1, the horizontal line y = -4 and the vertical lines x = 0 and x = 3. Find the volume of the solid generated when the region R is revolved about the line y = -4. You may use a calculator and round to the nearest thousandth. 20 15 10 5 y I I I | I + -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 -5 I -10 -15 I + I I T I I + -20 I + -25 I I I -30 I 3.5 4 xarrow_forwardplease show all the workarrow_forwardplease show all the workarrow_forward
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