2. Let S(x)==0and that for x € 1,(-1) k2k+1(2k+1)!∞S'(x) =>k=0for x € I. Prove that S is differentiable on I(-1) k2k(2k)!1x²2!+x44!

Answered: Image /qna-images/answer/b5e03507-a9a3-4ba7-a86c-615be1d6ac73.jpg

Answered: 2. Let S(x) = Σº (-1)+¹ for x € I.…

2. Let S(x) = Σº (-1)+¹ for x € I. Prove that S is differentiable on I k=0 (2k+1)! and that for x = I, ∞ S'(x) = Σ k=0 (-1) k2k x² (2k)! 1 x² 2! x4 4!

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 20E

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Question

2. Let S(x)==0
and that for x € 1,
(-1) k2k+1
(2k+1)!
∞
S'(x) =>
k=0
for x € I. Prove that S is differentiable on I
(-1) k2k
(2k)!
1
x²
2!
+
x4
4!

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