Consider the functions C: R → R and S: R → R defined by 00 C(x) = Σ n=0 2n (-1)" x ² (2n)! Use the Power Series to show that C'(x) C(0) = 1 and S(0) = 0 and S(x) == = Σ n=0 n 2n+1 (2n+1)! S(x) and S(x) = C(x) for all x & R and that

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