If $\displaystyle \lim_{x \to a} f(x) = L$, then $f(a) = L$

If $\displaystyle \lim_{x \to a} f(x) = L$, and $\displaystyle \lim_{x \to a} g(x) = L$ then $f(a)= g(a)$

The limit $\displaystyle \lim_{x \to a} \frac{f(x)}{g(x)}$ does not exist if $\displaystyle g(a)=0$