R, where / is an open interval containing the point c, and let ke r. prove the following. lett. 1 (a)f is differentiable at c with f(c) = k iff limh0 [fc +h)-f(c)] /h = k. (b) iffis differentiable at c with f(c) = k, then limh-0 [(fc + h) – f(c - h)]|2n = k. (c) if. f is differentiable at c with f(c) = k, then limno n[fc + 1/ n) - f(c)] = k. (d) find counterexamples to show that the converses of parts (b) and (c) are not true.