Question 3 For an arbitrary function f define f*(z) = lim f ( z + h) - f(z -h) h -+ 0+ 2h if this limit exists. Let P be defined by P(x) = cos(1/x) if x #0 10 if x = 0 and show that P*(0) = 0 even though P has no derivative at 0. ( You must also show that P has no derivative at 0, but can assume that P is not continuous at 0 to do this. )