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For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such e*, sin x, arctan x, and ln(1 +x). geometric series, binomial series, or the Maclaurin series for (a) If f(x) = (1 + x³)30, find f(58)(0). (b) If g(x) = sin(x³), find g(15)(0). (c) Suppose you know that f(x) is a function such that the Taylor series of f centered at 4 converges to f (x) for all x in the interval of convergence. If (-1)"n! (а-1)"(п+ 1) f(^(a) = show that the fifth degree Taylor polynomial centered at 4 approximates f(5) with error less than 0.0002.

For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such e*, sin x, arctan x, and ln(1 +x). geometric series, binomial series, or the Maclaurin series for (a) If f(x) = (1 + x³)30, find f(58)(0). (b) If g(x) = sin(x³), find g(15)(0). (c) Suppose you know that f(x) is a function such that the Taylor series of f centered at 4 converges to f (x) for all x in the interval of convergence. If (-1)"n! (а-1)"(п+ 1) f(^(a) = show that the fifth degree Taylor polynomial centered at 4 approximates f(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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Can I please get the answers for b and c?

For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such as geometric series, binomial series, or the Maclaurin series for e*, sin x, arctan x, and ln(1 +x). (a) If f(x) = (1+x³)30, find f(58)(0). (b) If g(x) = sin(x³), find g(15)(0). (c) Suppose you know that f (x) is a function such that the Taylor series of f centered at 4 converges to f (x) for all x in the interval of convergence. If (-1)"n! flm)(a) = (а-1)"(п + 1)" show that the fifth degree Taylor polynomial centered at 4 approximates f(5) with error less than 0.0002.
Transcribed Image Text:For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such as geometric series, binomial series, or the Maclaurin series for e*, sin x, arctan x, and ln(1 +x). (a) If f(x) = (1+x³)30, find f(58)(0). (b) If g(x) = sin(x³), find g(15)(0). (c) Suppose you know that f (x) is a function such that the Taylor series of f centered at 4 converges to f (x) for all x in the interval of convergence. If (-1)"n! flm)(a) = (а-1)"(п + 1)" show that the fifth degree Taylor polynomial centered at 4 approximates f(5) with error less than 0.0002.
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