(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 +...
(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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Question
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
+...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d258625-edd0-4f06-8dfd-6b1a087f7728%2F351a85a3-0f33-4070-afa4-e17cbbc851e7%2F07jjaln_processed.png&w=3840&q=75)
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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