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Magazine Problem 398
For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow 1} \frac{x-1}{1-\cos (\pi x)} $$
Problem 398
Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. \(\lim _{x \rightarrow 1} \frac{x-1}{1-\cos (\pi x)}\)
Problem 399
Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. \(\lim _{x \rightarrow 1} \frac{e^{(x-1)}-1}{x-1}\)
Problem 399
For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow 1} \frac{e^{(x-1)}-1}{x-1} $$
Problem 400
For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow 1} \frac{(x-1)^{2}}{\ln x} $$
Problem 400
Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. \(\lim _{x \rightarrow 1} \frac{(x-1)^{2}}{\ln x}\)
Problem 401
For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow \pi} \frac{1+\cos x}{\sin x} $$
Problem 401
Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. \(\lim _{x \rightarrow \pi} \frac{1+\cos x}{\sin x}\)
Problem 402
For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow 0}\left(\csc x-\frac{1}{x}\right) $$
Problem 402
Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. \(\lim _{x \rightarrow 0}\left(\csc x-\frac{1}{x}\right)\)
