Let C(x) = 1 x 2 /2! + x 4 /4! x 6 /6! +

Question:

Let C(x) = 1 − x²/2! + x⁴/4! − x⁶/6! + · · · .

(a) Show that C(x) has an infinite radius of convergence.
(b) Prove that C(x) and ƒ(x) = cos x are both solutions of y" = −y with initial conditions y(0) = 1, y'(0) = 0. This Initial Value Problem has a unique solution, so we have C(x) = cos x for all x.

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