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1) Suppose we know that ƒ(¹)(4) = = (-1)^n! 3n(n+1) and the Taylor series of f centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth-degree Taylor polynomial approximates ƒ(5) with error less than 0.0002.

1) Suppose we know that ƒ(¹)(4) = = (-1)^n! 3n(n+1) and the Taylor series of f centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth-degree Taylor polynomial approximates ƒ(5) with error less than 0.0002.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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(-1)^n! 1) Suppose we know that f(n) (4) = and the Taylor series of f 3n (n+1) centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth-degree Taylor polynomial approximates f(5) with error less than 0.0002.
Transcribed Image Text:(-1)^n! 1) Suppose we know that f(n) (4) = and the Taylor series of f 3n (n+1) centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth-degree Taylor polynomial approximates f(5) with error less than 0.0002.
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