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# Approximating In 2 Consider the following three ways to ## Problem 49RE Chapter 9

Calculus: Early Transcendentals | 1st Edition

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Problem 49RE

Approximating In 2 Consider the following three ways to approximate In 2.

a. Use the Taylor series for In (1 + x) centered al 0 and evaluate it at x = 1(convergence was asserted in Table 9.5) write the resulting infinite series. resulting infinite series.

b. Use the Taylor series for In (1 − x) centered at 0 and the identity In . Write the resulting infinite series.

c. Use the property In (a/b) = In a − In b and the series of parts (a) and (b) to find the Taylor series for centered at 0.

d. At what value of x should the series in part (c) be evaluated to approximate In 2? Write the resulting infinite series for In 2.

e. Using four terms of the series, which of the three series derived in parts (a)-(d) gives the best approximation to In 2? Which series gives the worst approximation? Can you explain why?

Step-by-Step Solution:
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Infinite and Negative Words 2/9/17 Indefinite Words Algo – something, anything Alguien – someone, somebody, anyone Alguno/a(s), algun – some, any o…o – either, or siempre – always tambien – also, too Negative Words Nada – nothing, not anything Nadie – no one, nobody, not anybody Ninguno/a(s),...

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##### ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Series, infinite, resulting, Taylor, use. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 49RE from 9 chapter was answered, more than 230 students have viewed the full step-by-step answer. The answer to “Approximating In 2 Consider the following three ways to approximate In 2.a. Use the Taylor series for In (1 + x) centered al 0 and evaluate it at x = 1(convergence was asserted in Table 9.5) write the resulting infinite series. resulting infinite series.b. Use the Taylor series for In (1 ? x) centered at 0 and the identity In . Write the resulting infinite series.c. Use the property In (a/b) = In a ? In b and the series of parts (a) and (b) to find the Taylor series for centered at 0.d. At what value of x should the series in part (c) be evaluated to approximate In 2? Write the resulting infinite series for In 2.e. Using four terms of the series, which of the three series derived in parts (a)-(d) gives the best approximation to In 2? Which series gives the worst approximation? Can you explain why?” is broken down into a number of easy to follow steps, and 151 words. The full step-by-step solution to problem: 49RE from chapter: 9 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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