91Ó°ÊÓ

Use a table and/or graph to decide whether each limit exists. If a limit exists, find its value. \(\lim _{x \rightarrow \pi} \frac{\tan ^{2} x}{1+\sec x}\)

Determine each limit, if it exists. $$\lim _{x \rightarrow 0} \frac{\cos x+2 \sin x-1}{3 x}$$

Find the equation of the tangent line to the function \(f\) at the given point. Then graph the function and the tangent line together. $$f(x)=\frac{1}{2} x^{2}-2 \text { at }(2,0)$$

Evaluate each limit. (a) \(\lim _{x \rightarrow 4} \sqrt{x-3}\) (b) \(\lim _{x \rightarrow 2} \sqrt{x-3}\) (c) \(\lim _{x \rightarrow 3} \sqrt{x-3}\)

Find the equation of the tangent line to the function \(f\) at the given point. Then graph the function and the tangent line together. $$f(x)=x^{3} \text { at }(1,1)$$

Evaluate each limit. (a) \(\lim _{x \rightarrow 1^{-}} \sqrt{1-x}\) (b) \(\lim _{x \rightarrow 1^{+}} \sqrt{1-x}\) (c) \(\lim _{x \rightarrow 1} \sqrt{1-x}\)

Use a table and/or graph to decide whether each limit exists. If a limit exists, find its value. \(\lim _{x \rightarrow 0} \frac{e^{2 x}-1}{e^{x}-1}\)

Use a table and/or graph to decide whether each limit exists. If a limit exists, find its value. \(\lim _{x \rightarrow 1} \frac{\ln x}{x-1}\)

Evaluate each limit. (a) \(\lim _{x \rightarrow \infty} \sqrt[3]{x}\) (b) \(\lim _{x \rightarrow 0^{+}} \sqrt[3]{x}\) (c) \(\lim _{x \rightarrow 0} \sqrt[3]{x}\)

Evaluate each limit. (a) \(\lim _{x \rightarrow 0} \sqrt{4-x^{2}}\) (b) \(\lim _{x \rightarrow 3} \sqrt{4-x^{2}}\) (c) \(\lim _{x \rightarrow 2} \sqrt{4-x^{2}}\)