Let f be defined in a domain that contains the origin. The function f is said to be even if f(−z)=f(z), and it is called odd if f(−z)=−f(z).
((a)) Show that the derivative of an odd function is an even function.
((b)) Show that the derivative of an even function is an odd function. Hint: Use limits.
((c)) If f(z) is even, show that all the coefficients of the odd powers of z in the Maclaurin series are zero.
((d)) If f(z) is odd, show that all the coefficients of the even powers of z in the Maclaurin series are zero.