Choose the best reason that the function $$f(x)=\left\lbrace \begin{array}{ll} \frac{1}{x-7},& \quad {\rm if}\quad x\not=7, \\ 18,& \quad {\rm if} \quad x=7 \end{array}\right.$$ is discontinuous at $a=7$.

A. $\displaystyle \lim_{x\to a} f(x)\not = f(a)$

B. $\displaystyle \lim_{x\to a} f(x)$ doesn't exist

C. The function is not defined at the point given.

Answer: ? A B C .