91Ó°ÊÓ

Evaluate each limit. $$\begin{array}{l} \text { (a) } \lim _{x \rightarrow 0^{-}} \log |x| \\ \text { (b) } \lim _{x \rightarrow 0^{+}} \log |x| \\ \text { (c) } \lim _{x \rightarrow 0} \log |x| \end{array}$$

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

Evaluate each limit. (a) \(\lim _{x \rightarrow 4^{-}} \frac{x-4}{|x-4|}\) (b) \(\lim _{x \rightarrow 4^{+}} \frac{x-4}{|x-4|}\) (c) \(\lim _{x \rightarrow 4} \frac{x-4}{|x-4|}\)

Evaluate each limit. (a) \(\lim _{x \rightarrow 9} e^{\sqrt{x}}\) (b) \(\lim _{x \rightarrow-2} e^{\sqrt{x}}\) (c) \(\lim _{x \rightarrow 0} e^{\sqrt{x}}\)

Find \(f^{\prime}(x)\) using the alternative definition. $$f(x)=-3 x^{2}+1$$

Use a table and/or graph to decide whether each limit exists. If a limit exists, find its value. \(\lim _{x \rightarrow 0}(x \ln |x|)\)

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

Write an expression for a function \(f(x)\) with the given features. \(f(x)\) is a quotient of two polynomials of degree greater than \(2, \lim _{x \rightarrow \infty} f(x)=0\)

Find \(f^{\prime}(x)\) using the alternative definition. $$f(x)=x^{2}+3 x-2$$

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