Let $\displaystyle \lim_{ x \rightarrow a} f(x) = 2$ , $\displaystyle \lim_{ x \rightarrow a} h(x)= -6$, $\displaystyle \lim_{ x \rightarrow a} g(x) = 0$.

Find following limits if they exist. If not, enter DNE ('does not exist') as your answer.

 1. $\displaystyle \lim_{ x \rightarrow a} \frac{1}{h(x)-g(x)}$
 2. $\displaystyle \lim_{ x \rightarrow a} \frac{f(x)} {g(x)}$
 3. $\displaystyle \lim_{ x \rightarrow a} (h(x))^{-1}$
 4. $\displaystyle \lim_{ x \rightarrow a} \frac{f(x)} {h(x)}$
 5. $\displaystyle \lim_{ x \rightarrow a} f(x)+h(x)$
 6. $\displaystyle \lim_{ x \rightarrow a} \sqrt{h(x)}$