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(1) Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn(x) → 0). f(x)=√√x, a = 4 *Note: it may be difficult to find a closed formula for the terms of Taylor series, so writing out four or five terms and a good faith effort to find this formula is sufficient. (2) Use a known Maclaurin series to obtain the Maclaurin series for f(x) = sin²x. (Hint: Use sin²x = = (1 - cos(2x)))

(1) Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn(x) → 0). f(x)=√√x, a = 4 *Note: it may be difficult to find a closed formula for the terms of Taylor series, so writing out four or five terms and a good faith effort to find this formula is sufficient. (2) Use a known Maclaurin series to obtain the Maclaurin series for f(x) = sin²x. (Hint: Use sin²x = = (1 - cos(2x)))

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 44E
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(1) Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn (x) → 0). f(x)=√x, a = 4 *Note: it may be difficult to find a closed formula for the terms of Taylor series, so writing out four or five terms and a good faith effort to find this formula is sufficient. (2) Use a known Maclaurin series to obtain the Maclaurin series for f(x) = sin²x. (Hint: Use sin² x = = (1 - cos(2x)))
Transcribed Image Text:(1) Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn (x) → 0). f(x)=√x, a = 4 *Note: it may be difficult to find a closed formula for the terms of Taylor series, so writing out four or five terms and a good faith effort to find this formula is sufficient. (2) Use a known Maclaurin series to obtain the Maclaurin series for f(x) = sin²x. (Hint: Use sin² x = = (1 - cos(2x)))
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