Let f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1 a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1 b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1 c. Determine the interval of convergence for the series given in (b).
Let f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1 a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1 b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1 c. Determine the interval of convergence for the series given in (b).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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Let f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1
a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1
b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1
c. Determine the interval of convergence for the series given in (b).
d. Use the series for f about x=1 to determine if the graph of f has any points of inflection.
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