Explanation Given Info: a and b are both positive or negative But not if a < 0 and b > 0 f is continuous on [ a , b ] and differentiable on [ a , b ] Any point c ∈ [ a , b ] Formula Used: f ( c ) = f ( b ) − f ( a ) b − a a = − 2 , b = 1 , f ( a ) = − 1 , f ( b ) = 0 , b − a = 3 C a l c u l a t i o n :

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 4.3, Problem 57E

To determine

To find f(x)=1−|x| satisfies the conclusion of the MVT on [a,b].

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Chapter 4.3, Problem 56E

Chapter 4.3, Problem 58E

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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 = Need Help? Read It Watch It SUBMIT ANSWER

Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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To find f ( x ) = 1 − | x | satisfies the conclusion of the MVT on [ a , b ] .

Solution Summary: The author explains that f(x)=1-left|xright| satisfies the conclusion of the MVT.

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To find f(x)=1−|x| satisfies the conclusion of the MVT on [a,b].

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Chapter 4 Solutions