5. Consider the function defined by f(x) = e²-¹. a. Determine the Taylor series expansion of f at x = 1. b. Using the first four terms of the Taylor series, approximate 1/e.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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5. Consider the function defined by ƒ(x) = ex²-¹.
a. Determine the Taylor series expansion of ƒ at x
=
b. Using the first four terms of the Taylor series, approximate 1/e.
= 1.
Transcribed Image Text:5. Consider the function defined by ƒ(x) = ex²-¹. a. Determine the Taylor series expansion of ƒ at x = b. Using the first four terms of the Taylor series, approximate 1/e. = 1.
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