If $ f(x) $ is differentiable at $ x = a $, then consider the following statements : I. $ f(x) $ is continuous at $ x = a $ II. $ \lim_{x \to a} f(x) = f(a) $ Which of the statements given above is/are correct ?

Question

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Both I and II. Differentiability at a point implies continuity at that point. Continuity by definition means the limit of the function as x approaches a equals the function's value at a.

Answer

I only

Answer

II only

Answer

Neither I nor II

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

Explanation

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