Suppose $$\lim_{x\rightarrow a} h(x) = 0, \ \ \lim_{x\rightarrow a} f(x) = 8, \ \ \lim_{x\rightarrow a} g(x) = 9.$$

Find following limits if they exist. Enter DNE if the limit does not exist.

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