To determine The first four terms of the Maclaurin series expansion for the given function. Explanation Maclaurin series expansion: f ( x ) = f ( 0 ) + f ′ ( 0 ) x + f ″ ( 0 ) x 2 2 ! + f ‴ ( 0 ) x 3 3 ! + … + f n ( 0 ) x n n ! + … . Calculation: The given function is, f ( x ) = 1 1 + x . Differentiate the above function with respect to x . f ′ ( x ) = d d x ( 1 1 + x ) = − 1 ( 1 + x ) 2 d d x ( 1 + x ) ( ∵ d d x ( 1 v n ) = − n v n + 1 d d x ( v ) ) = − 1 ( 1 + x ) 2 ( 1 ) = − 1 ( 1 + x ) 2 Again, differentiate the function f ′ ( x ) with respect to x . f ″ ( x ) = d d x ( − 1 ( 1 + x ) 2 ) = − ( ( − 2 ) ( 1 + x ) 3 d d x ( 1 + x ) ) ( ∵ d d x ( 1 v n ) = − n v n + 1 d d x ( v ) ) = 2 ( 1 + x ) 3 ( 1 ) = 2 ( 1 + x ) 3 In the same way, differentiate the function f ″ ( x ) with respect to x

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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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 30.2, Problem 1PE

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The first four terms of the Maclaurin series expansion for the given function.

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Chapter 30.1, Problem 48E

Chapter 30.2, Problem 1E

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Chapter 30 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 30.1 - Prob. 1PE Ch. 30.1 - Prob. 2PE Ch. 30.1 - Prob. 1E Ch. 30.1 - Prob. 2E Ch. 30.1 - Prob. 3E Ch. 30.1 - Prob. 4E Ch. 30.1 - Prob. 5E Ch. 30.1 - Prob. 6E Ch. 30.1 - Prob. 7E Ch. 30.1 - Prob. 8E

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