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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.

$\lim_{x\to {0}^{+}}{x}^{2}\ln x$

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.

$\lim_{x\to \infty }{x}^{1/x}$

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’Hôpital’s rule.

$\lim_{x\to 0}{x}^{2/x}$

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’Hôpital’s rule.

$\lim_{x\to 0}\frac{{x}^{2}}{1/x}$

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’Hôpital’s rule.

$\lim_{x\to \infty }\frac{{e}^{x}}{x}$

The definite integral was defined with what two stipulations?

If $\displaystyle \lim_{b\to \infty} \int_0^b f(x)\ dx$ exists, then the integral $\displaystyle \int_0^\infty f(x)\ dx$ is said to _____.

If $\displaystyle \int_1^\infty f(x)\ dx=10$, and $0\leq g(x)\leq f(x)$ for all $x$, then we know that $\displaystyle \int_1^\infty g(x)\ dx$ _____.

For what values of $p$ will $\displaystyle \int_1^\infty \frac1{x^p}\ dx$ converge?

For what values of $p$ will $\displaystyle \int_{10}^\infty \frac1{x^p}\ dx$ converge?

For what values of $p$ will $\displaystyle \int_{0}^1 \frac1{x^p}\ dx$ converge?