Explanation Given: The given function is, f ( x ) = { e − 1 / x 2 , x ≠ 0 , 0 , x = 0 Approach: The Taylor series expansion about a point x 0 is given by, f ( x ) = f ( x 0 ) + ( x − x 0 ) f ′ ( x 0 ) + ( x − x 0 ) 2 2 ! f ″ ( x 0 ) + ( x − x 0 ) 3 3 ! f ‴ ( x 0 ) + ... When x 0 = 0 the series, f ( x ) = f ( 0 ) + ( x ) f ′ ( 0 ) + ( x ) 2 2 ! f ″ ( 0 ) + ( x ) 3 3 ! f ‴ ( 0 ) + ... is said to be the Maclaurin’s series. Calculation: The given function is, f ( x ) = { e − 1 / x 2 , x ≠ 0 , 0 , x = 0 f ( 0 ) = 0

Fundamentals of Differential Equations and Boundary Value Problems

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ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 8.2, Problem 37E

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The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.

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Chapter 8.2, Problem 36E

Chapter 8.2, Problem 38E

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The Maclaurin series for given f ( x ) is 0 + 0 + 0 + ... , which converges for all x but is equal to f ( x ) only when x = 0 .

Solution Summary: The author explains how the Maclaurin series for given f(x) is converged for all

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The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.

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Chapter 8 Solutions

The Maclaurin series for given f ( x ) is 0 + 0 + 0 + ... , which converges for all x but is equal to f ( x ) only when x = 0 .

Solution Summary: The author explains how the Maclaurin series for given f(x) is converged for all

Videos

To show: The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.

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Chapter 8 Solutions

To show:

The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.