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a) Consider the function arctan(r). Nrite a partial sum for the power series which represents this function consisting of the first 1+ 3 + 3z + 3³z. Also indicate the radius of convergence. Partial Sum: Radius of Convergence: ) Use part a) to write the partial sum for the power series which represents farctan(a) Nrite the first 4 nonzero terms. Also indicate the radius of convergence. Partial Sum: Radius of Convergence:

a) Consider the function arctan(r). Nrite a partial sum for the power series which represents this function consisting of the first 1+ 3 + 3z + 3³z. Also indicate the radius of convergence. Partial Sum: Radius of Convergence: ) Use part a) to write the partial sum for the power series which represents farctan(a) Nrite the first 4 nonzero terms. Also indicate the radius of convergence. Partial Sum: Radius of Convergence:

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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a) Consider the function arctan(r?). Write a partial sum for the power series which represents this function consisting of the first 4 nonzero terms. For example, if the series were 3"2n you would write 1+ 3x² + 3?x“ + 33x°. Also indicate the radius of convergence. Ln=0 Partial Sum: Radius of Convergence: b) Use part a) to write the partial sum for the power series which represents farctan(r)dr. Write the first 4 nonzero terms. Also indicate the radius of convergence. Partial Sum: Radius of Convergence: -0.6 c) Use part b) to approximate the integral o arctan(r)dr.
Transcribed Image Text:a) Consider the function arctan(r?). Write a partial sum for the power series which represents this function consisting of the first 4 nonzero terms. For example, if the series were 3"2n you would write 1+ 3x² + 3?x“ + 33x°. Also indicate the radius of convergence. Ln=0 Partial Sum: Radius of Convergence: b) Use part a) to write the partial sum for the power series which represents farctan(r)dr. Write the first 4 nonzero terms. Also indicate the radius of convergence. Partial Sum: Radius of Convergence: -0.6 c) Use part b) to approximate the integral o arctan(r)dr.
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