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? If lim f(x) - f(a) O =L, then x - a lim f(x) = f(a) . r+a O If f is differentiable at x - a, then f is continuous at x = a. If lim f(x) - f(a) exists, then O r+a r - a lim f(x) = lim f(x). r-+a If f is differentiable at x = a, then lim f(x) may not exist. r-+a None of the above Section Attempt 1 of 1 Verify