Let a > 0 and suppose that f C(-a, a). a) If f is odd [i.e.,

Question:

Let a > 0 and suppose that f ∈ C∞(-a, a).
a) If f is odd [i.e., if (-x) = -f(x) for all x ∈ (-a, a)], then the Maclaurin series of f contains only odd powers of x.
b) If f is even [i.e., if f(-x) = f(x) for all x ∈ (-a, a)], then the Maclaurin series of f contains only even powers of x.