91Ó°ÊÓ

Evaluate the limit. Evaluate the limit \(\lim _{x \rightarrow a} \frac{x-a}{x^{2}-a^{2}}, \quad a \neq 0\).

Evaluate the limit. Evaluate the limit \(\lim _{x \rightarrow a} \frac{x-a}{x^{3}-a^{3}}, \quad a \neq 0\).

Evaluate the limit. Evaluate the limit \(\lim _{x \rightarrow a} \frac{x-a}{x^{n}-a^{n}}, \quad a \neq 0\).

Determine whether you can apply L'Hôpital's rule directly. Explain why or why not. Then, indicate if there is some way you can alter the limit so you can apply L'Hôpital's rule. \(\lim _{x \rightarrow 0^{+}} x^{2} \ln x\)

For the following exercises, determine whether you can apply L'Hôpital's rule directly. Explain why or why not. Then, indicate if there is some way you can alter the limit so you can apply L'Hôpital's rule. $$ \lim _{x \rightarrow 0^{+}} x^{2} \ln x $$

For the following exercises, determine whether you can apply L'Hôpital's rule directly. Explain why or why not. Then, indicate if there is some way you can alter the limit so you can apply L'Hópital's rule. $$ \lim _{x \rightarrow \infty} x^{1 / x} $$

Determine whether you can apply L'Hôpital's rule directly. Explain why or why not. Then, indicate if there is some way you can alter the limit so you can apply L'Hôpital's rule. \(\lim _{x \rightarrow \infty} x^{1 / x}\)

For the following exercises, determine whether you can apply L'Hôpital's rule directly. Explain why or why not. Then, indicate if there is some way you can alter the limit so you can apply L'Hópital's rule. $$ \lim _{x \rightarrow 0} x^{2 / x} $$

Determine whether you can apply L'Hôpital's rule directly. Explain why or why not. Then, indicate if there is some way you can alter the limit so you can apply L'Hôpital's rule. \(\lim _{x \rightarrow 0} x^{2 / x}\)

For the following exercises, determine whether you can apply L'Hôpital's rule directly. Explain why or why not. Then, indicate if there is some way you can alter the limit so you can apply L'Hópital's rule. $$ \lim _{x \rightarrow 0} \frac{x^{2}}{1 / x} $$