Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Chapter 4.4, Problem 4C
To determine
To explain: The reason for calling the collection of anti derivatives of a function f a
family and to explain relation between anti-derivatives of a function related.
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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 - 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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 - 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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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- do question 2 pleasearrow_forwardquestion 10 pleasearrow_forward00 (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 շոarrow_forward
- (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 = Need Help? Read It Watch It SUBMIT ANSWERarrow_forwardanswer for question 4 pleasearrow_forward(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}. (a) (2 points) Calculate the divergence V. F. (b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that the triple integral √ (V · F) dV = √ 2²(1. = x²(1 − x² - y²) dA. Earrow_forward
- (2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy). (a) (2 points) Calculate V. F. (b) (6 points) Given a vector field is everywhere defined with V G₁(x, y, z) = * G2(x, y, z) = − G3(x, y, z) = 0. 0 0 F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that F = 0, let G = (G1, G2, G3) where F₂(x, y, y, t) dt - √ F³(x, t, 0) dt, * F1(x, y, t) dt, t) dt - √ F Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √ √(x + y) A R R = {(x, y) | 25 < x² + y² ≤ 36, x < 0} Hint: The integral and Region is defined in rectangular coordinates.arrow_forwardFind 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_forward
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