第1862题：Limits and derivatives

The right proposition in the following propositions is (  ).

A. If $\lim\limits_{x \to a} f(x) =f(a)$ then $f'(a)$ exists.

B. If $\lim\limits_{x \to a} f(x) \ne f(a)$ then $f'(a)$ dose not exists.

C. If $f'(a)$ dose not exist then $\lim\limits_{x \to a} f(x) \ne f(a)$ .

D.If $f'(a)$ dose not exist then cure $y=f(x)$ does not have tangent at $(a, f(a))$ .