Consider the function f(x) = ln(1 + x) and its Taylor series about x = 0....
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Consider the function f(x) = ln(1 + x) and its Taylor series about x = 0. a. [4 points] Determine the first four non-zero terms of the Taylor series for f(x) = ln(1+x) about x = 0. Be sure to show enough work to support your answer. b. [4 points] Find the first three non-zero terms of the Taylor series for g(x) = ln (1) about x = 0. Be sure to show enough work to support your answer. (Hint: You may find it helpful to utilize properties of logarithms.) c. [2 points] Find the exact value of the sum of the series 3 5 3 2 3 ²(Q) + (O)² + (0)² +-· 2 2 3 5 +.... 4 3 4 4 Consider the function f(x) = ln(1 + x) and its Taylor series about x = 0. a. [4 points] Determine the first four non-zero terms of the Taylor series for f(x) = ln(1+x) about x = 0. Be sure to show enough work to support your answer. b. [4 points] Find the first three non-zero terms of the Taylor series for g(x) = ln (1) about x = 0. Be sure to show enough work to support your answer. (Hint: You may find it helpful to utilize properties of logarithms.) c. [2 points] Find the exact value of the sum of the series 3 5 3 2 3 ²(Q) + (O)² + (0)² +-· 2 2 3 5 +.... 4 3 4 4
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Posted Date:
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