2. The Maclaurin series expansion of tan-¹r is given by tan Σ x = n=0 (-1)" (2n + 1) Use the sixth degree Maclaurin polynomial for r tan ¹2 to approximate (2) -1 your answer as a single fraction in lowest terms). 2n+1 for x € (-1, 1). ¹ (¹) tan-1 (express

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 22RE
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+00
(-1)"
2. The Maclaurin series expansion of tan
Σ
22n+1 for r E (-1,1).
-1
a is given by tan
-1
x =
(2n + 1)
n=0
(3)
(;)
Use the sixth degree Maclaurin polynomial for x tan-a to approximate
tan-1
(еxpress
your answer as a single fraction in lowest terms).
W!
Transcribed Image Text:+00 (-1)" 2. The Maclaurin series expansion of tan Σ 22n+1 for r E (-1,1). -1 a is given by tan -1 x = (2n + 1) n=0 (3) (;) Use the sixth degree Maclaurin polynomial for x tan-a to approximate tan-1 (еxpress your answer as a single fraction in lowest terms). W!
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How did you get the expression for xtan^-1(x)? How did you relate it with the maclaurin series of tan^-1 x?

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