If f(x) is differentiable at x = a, then consider the following statements: I. f(x) is continuous at x = a. II. lim(x→a) f(x) = f(a). Which of the statements given above is/are correct?

Question

Accepted Answer

Both I and II. Differentiability at x = a implies continuity at x = a, so statement I is correct. Continuity at x = a means lim(x→a) f(x) = f(a), which is exactly statement II. Therefore both statements I and II are correct.

If f(x) is differentiable at x = a, then consider the following statements: I. f(x) is continuous at x = a. II. lim(x→a) f(x) = f(a). Which of the statements given above is/are correct?

Explanation

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