Use the result of Example 7 to show that is an antiderivative of (x) = tan 1

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Use the result of Example 7 to show that

EXAMPLE 7 Power Series for Arctangent Prove that for -1 < x < 1. 15 x7 + 3 5 7 00 (-1)xm+1 2n + 1 tan- x =

F(x) = 12 1.2 14 3.4 + 15 5.6 18 7.8

is an antiderivative of ƒ(x) = tan⁻¹ x satisfying F(0) = 0. What is the radius of convergence of this power series?

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 19, 2023 08:07 AM

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Use the result of Example 7 to show that is an antiderivative of (x) = tan 1

Question:

EXAMPLE 7 Power Series for Arctangent Prove that for -1 < x < 1. 15 x7 + 3 5 7 00 (-1)²x²m+1 2n + 1 tan- x = Σ n=0 =X

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For 1 x 1 which is the interval of convergence for the power series for arc...View the full answer

Calculus

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