From Exercise 24 we know the following series converges for all x. We define g(x) to be
Chapter 9, Problem 47(choose chapter or problem)
From Exercise 24 we know the following series converges for all x. We define g(x) to be its sum: g(x) = + n=1 (1)n1 x2n1 (2n 1)!. (a) Is g(x) odd, even, or neither? What is g(0)? (b) Assuming that derivatives can be computed term by term, show that g(x) = g(x). (c) Guess what well-known function g might be. Check your guess using g(0) and g (0).
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