(a) Use the fact that dtan to find a Taylor series for tan-1 x. dx (b) Using the Taylor series you derive in part (a), obtain Leibniz's formula: -1 = ㅠ 4 = 1 1 1 + 3 5 1 7 +...

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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please do both part a and b

(a) Use the fact that d tan-¹₁
dx
=
1+2 to find a Taylor series for tan-¹x.
1+x²
(b) Using the Taylor series you derive in part (a), obtain Leibniz's formula:
ㅠ
4
= 1
1 1
+
3 5
-
1
7
+...
Transcribed Image Text:(a) Use the fact that d tan-¹₁ dx = 1+2 to find a Taylor series for tan-¹x. 1+x² (b) Using the Taylor series you derive in part (a), obtain Leibniz's formula: ㅠ 4 = 1 1 1 + 3 5 - 1 7 +...
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