91Ó°ÊÓ

Find the average rate of change of the function over the given interval or intervals. \(f(x)=x^{3}+1\) a. [2,3] b. [-1,1]

Sketch the interval \((a, b)\) on the \(x\) -axis with the point \(c\) inside. Then find a value of \(\delta>0\) such that for all \(x, 0<|x-c|<\delta \Rightarrow a

Find the average rate of change of the function over the given interval or intervals. \(g(x)=x^{2}-2 x\) a. [1,3] b. [-2,4]

Sketch the interval \((a, b)\) on the \(x\) -axis with the point \(c\) inside. Then find a value of \(\delta>0\) such that for all \(x, 0<|x-c|<\delta \Rightarrow a

Find the average rate of change of the function over the given interval or intervals. \(h(t)=\cot t\) a. \([\pi / 4,3 \pi / 4]\) b. \([\pi / 6, \pi / 2]\)

Sketch the interval \((a, b)\) on the \(x\) -axis with the point \(c\) inside. Then find a value of \(\delta>0\) such that for all \(x, 0<|x-c|<\delta \Rightarrow a

Find the limit of each function (a) as \(x \rightarrow \infty\) and (b) as \(x \rightarrow-\infty\). (You may wish to visualize your answer with a graphing calculator or computer.) $$f(x)=\frac{2}{x}-3$$

$$\text { Let } f(x)=\left\\{\begin{array}{ll}3-x, & x<2 \\\2, & x=2 \\\\\frac{x}{2}, & x>2\end{array}\right.$$ a. Find \(\lim _{x \rightarrow 2^{+}} f(x), \lim _{x \rightarrow 2^{-}} f(x),\) and \(f(2)\) b. Does \(\lim _{x \rightarrow 2} f(x)\) exist? If so, what is it? If not, why not? c. Find \(\lim _{x \rightarrow-1^{-}} f(x)\) and \(\lim _{x \rightarrow-1^{+}} f(x)\) d. Does \(\lim _{x \rightarrow-1} f(x)\) exist? If so, what is it? If not, why not?

Find the limit of each function (a) as \(x \rightarrow \infty\) and (b) as \(x \rightarrow-\infty\). (You may wish to visualize your answer with a graphing calculator or computer.) $$f(x)=\pi-\frac{2}{x^{2}}$$

Sketch the interval \((a, b)\) on the \(x\) -axis with the point \(c\) inside. Then find a value of \(\delta>0\) such that for all \(x, 0<|x-c|<\delta \Rightarrow a