Explanation Formula used: Maclaurin expansion of e x : “The Maclaurin expansion of e x is given by, e x = 1 + x + x 2 2 ! + x 3 3 ! + x 4 4 ! + ⋯ ” Taylor series expansion of a function: f ( x ) = f ( a ) + f ′ ( a ) ( x − a ) + f ″ ( a ) ( x − a ) 2 2 ! + … . Calculation: Replace x by 0.9 in the Maclaurin expansion of e x and obtain the Maclaurin expansion of e 0.9 as follows. e 0.9 = 1 + ( 0.9 ) + ( 0.9 ) 2 2 ! + ( 0.9 ) 3 3 ! + ⋯ = 1.9 + 0.81 2 + 0.729 6 + ⋯ = 1.9 + 0.405 + 0.1215 + ⋯ = 2.4265 Therefore, the value of e 0.9 using Maclaurin expansion of e x is 2.4265 _ . Consider the function f ( x ) = e x with a = 1 . The derivatives and its values are shown in below table. f ( x ) = e x f ( 1 ) = e 1 f ′ ( x ) = e x f ′ ( 1 ) = e 1 f ″ ( x ) = e x f ″ ( 1 ) = e 1 f ‴ ( x ) = e x f ‴ ( 1 ) = e 1 The Taylor series expansion of the given function f ( x ) = e x is written as follows

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Author: Washington

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Chapter 30, Problem 65RE

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The value of e0.9 using the Maclaurin expansion of ex and using Taylor expansion.

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Chapter 30, Problem 64RE

Chapter 30, Problem 66RE

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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 value of e 0.9 using the Maclaurin expansion of e x and using Taylor expansion. Also compare the values with the value obtained using calculator.

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The value of e0.9 using the Maclaurin expansion of ex and using Taylor expansion. Also compare the values with the value obtained using calculator.

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The value of e0.9 using the Maclaurin expansion of ex and using Taylor expansion.

Also compare the values with the value obtained using calculator.