91Ó°ÊÓ

Use a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. \(\lim _{x \rightarrow 0^{+}} \tan \left(x^{x}\right)\)

For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. $$ \lim _{x \rightarrow 0^{+}} \tan \left(x^{x}\right) $$

Use a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. \(\lim _{x \rightarrow 0^{+}} \frac{\ln x}{\sin x}\)

For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. $$ \lim _{x \rightarrow 0^{+}} \frac{\ln x}{\sin x} $$

Use a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. \(\lim _{x \rightarrow 0} \frac{e^{x}-e^{-x}}{x}\)

For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. $$ \lim _{x \rightarrow 0} \frac{e^{x}-e^{-x}}{x} $$

Write Newton's formula as \(x_{n+1}=F\left(x_{n}\right)\) for solving \(f(x)=0\). \(f(x)=x^{2}+1\)

For the following exercises, write Newton's formula as \(x_{n+1}=F\left(x_{n}\right)\) for solving \(f(x)=0.\) $$f(x)=x^{2}+1$$

Write Newton's formula as \(x_{n+1}=F\left(x_{n}\right)\) for solving \(f(x)=0\). \(f(x)=x^{3}+2 x+1\)

For the following exercises, write Newton's formula as \(x_{n+1}=F\left(x_{n}\right)\) for solving \(f(x)=0.\) $$f(x)=x^{3}+2 x+1$$