Explanation Formula used: Maclaurin expansion of ( 1 + x ) n : “The Maclaurin expansion of ( 1 + x ) n is given by, ( 1 + x ) n = 1 + n x + n ( n − 1 ) 2 ! x 2 + n ( n − 1 ) ( n − 2 ) 3 ! x 3 + ⋯ ” Calculation: Rewrite the functions 1 1 − x and 1 1 + x as follows. 1 1 − x = ( 1 + ( − x ) ) − 1 and 1 1 + x = ( 1 + x ) − 1 Replace x by − x and n by –1 in the Maclaurin expansion of ( 1 + x ) n and obtain the Maclaurin expansion of ( 1 − x ) − 1 as shown below. ( 1 + ( − x ) ) − 1 = 1 − 1 ( − x ) + − 1 ( − 1 − 1 ) 2 ! ( − x ) 2 + − 1 ( − 1 − 1 ) ( − 1 − 2 ) 3 ! ( − x ) 3 + ⋯ = 1 + x + 2 2 x 2 + 6 6 x 3 + ⋯ = 1 + x + x 2 + x 3 + ⋯ Now replace n by –1 in the Maclaurin expansion of ( 1 + x ) n and obtain the Maclaurin expansion of ( 1 + x ) − 1 as shown below

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Chapter 30.3, Problem 17E

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The Maclaurin expansion of f(x)=21−x2 by adding the series for 11−x and 11+x.

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Chapter 30.3, Problem 16E

Chapter 30.3, Problem 18E

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Chapter 30 Solutions

Basic Technical Mathematics

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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The Maclaurin expansion of f ( x ) = 2 1 − x 2 by adding the series for 1 1 − x and 1 1 + x .

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The Maclaurin expansion of f(x)=21−x2 by adding the series for 11−x and 11+x.

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