3. Show that the following two definitions of differentiability are equivalent. (a) The function f is differentiable at r = a if and only if the limit L = lim Ar-0 f(x+ Az) – f(x) Ar exists. In this...

Extracted text: 3. Show that the following two definitions of differentiability are equivalent. (a) The function f is differentiable at r = a if and only if the limit L = lim Ar-0 f(x+ Az) – f(x) Ar exists. In this case we define f'(a) = L. (b) The function f is differentiable at z = a if and only if there is a constant m and a function E of z, defined for all z + a satisfying the two conditions f(x) = f(a) + m(x = a) + E(x)(z – a) for all z # a, lim E(r) = 0. In this case we define f'(a) = m.