Consider tan-1 x =+∞Σn=0(-1)²n+12n + 1for all x € [-1,1].a. By differentiating tan-¹ (2²), find a power series representation of f(x)€ (-1,1).c. Approximate tanb. Use the result in item a. to find the exact value of+∞n=0(−1)n+116n=2x1+xªthat is valid for all¹) using a 4th degree Maclaurin polynomial.Hint: Using the power series representation for tan given above, write x tan¹ as a power series.

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Consider tan-1 x = C. +∞ n=0 (-1)¹x²n+1 2n + 1 for all x € [-1,1]. a. By differentiating tan−¹(x²), find a power series representation of f(x) € (-1,1). +∞o b. Use the result in item a. to find the exact value of n=0 (−1)n+1 16n Approximate (tan-¹¹) using a 4th degree Maclaurin polynomial. Hint: Using the power series representation for tan¹ given above, write a tan -1 2x 1+x¹ that is valid for all as a power series.

Consider tan-1 x = C. +∞ n=0 (-1)¹x²n+1 2n + 1 for all x € [-1,1]. a. By differentiating tan−¹(x²), find a power series representation of f(x) € (-1,1). +∞o b. Use the result in item a. to find the exact value of n=0 (−1)n+1 16n Approximate (tan-¹¹) using a 4th degree Maclaurin polynomial. Hint: Using the power series representation for tan¹ given above, write a tan -1 2x 1+x¹ that is valid for all as a power series.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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