please solve the following question and include explanation. ( ignore the answer shown in the picture, as it is just the automatic answer (may be correct or false)

Which of the following statements are true? A piecewise function cannot be O differentiable. If f is differentiable at x = a, then V lim f(x) exists. f(x) - f(a) If lim = L, then O x - a lim f(x) = f(a) . V If f is differentiable at * = a, then f is continuous at x = a. O None of the above