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!
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!
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Transcribed Image Text: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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