91Ó°ÊÓ

Precalculus and Calculus Describe the relationship between precalculus and calculus. List three precalculus concepts and their corresponding calculus counterparts.

Polynomial Function Describe how to find the limit of a polynomial function \(p(x)\) as \(x\) approaches \(c .\)

Secant and Tangent Lines Discuss the relationship between secant lines through a fixed point and a corresponding tangent line at that fixed point.

Secant Lines Consider the function \(f(x)=\sqrt{x}\) and the point \(P(4,2)\) on the graph of \(f .\) (a) Graph \(f\) and the secant lines passing through \(P(4,2)\) and \(Q(x, f(x))\) for \(x\) -values of \(1,3,\) and \(5 .\) (b) Find the slope of each secant line. (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of \(f\) at \(P(4,2) .\) Describe how to improve your approximation of the slope.

Finding a Limit of a Trigonometric Function In Exercises \(27-36,\) find the limit of the trigonometric function. $$\lim _{\rightarrow \pi / 2} \sin x$$

Continuity on a Closed Interval In Exercises 35-38, discuss the continuity of the function on the closed interval. \(\begin{array}{ll}{\text { Function }} & {\text { Interval }} \\\ {g(x)=\sqrt{49-x^{2}}} & {[-7,7]}\end{array}\)

Continuity on a Closed Interval In Exercises 35-38, discuss the continuity of the function on the closed interval. \(\begin{array}{ll}{\text { Function }} & {\text { Interval }} \\ \\\ {f(l)=3-\sqrt{9-l^{2}}} & {[-3,3]}\end{array}\)

Evaluating Limits In Exercises \(37-40,\) use the information to evaluate the limits. $$\begin{array}{l}{\lim _{x \rightarrow c} f(x)=2} \\ {\lim _{x \rightarrow c} g(x)=\frac{3}{4}} \\ {\text { (a) } \lim _{x \rightarrow c}[4 f(x)]} \\\ {\text { (b) } \lim _{x \rightarrow c}[f(x)+g(x)]} \\ {\text { (c) } \lim _{x \rightarrow c}[f(x) g(x)]} \\ {\text { (d) } \lim _{x \rightarrow c} \frac{f(x)}{g(x)}}\end{array}$$

Evaluating Limits In Exercises \(37-40,\) use the information to evaluate the limits. $$\begin{array}{l}{\lim _{x \rightarrow c} f(x)=16} \\ {\text { (a) } \lim _{r \rightarrow \infty}[f(x)]^{2}} \\ {\text { (b) } \lim _{x \rightarrow c} \sqrt{f(x)}} \\ {\text { (c) } \lim _{x \rightarrow c}[3 /(x)]} \\ {\text { (d) } \lim _{x \rightarrow c}[f(x)]^{3 / 2}}\end{array} $$

On a trip of \(d\) miles to another city, a truck driver's average speed was \(x\) miles per hour. On the return trip, the average speed was \(y\) miles per hour. The average speed for the round trip was 50 miles per hour. (a) Verify that $$\begin{array}{l}{y=\frac{25 x}{x-25}} \\ {\text { What is the domain? }}\end{array}$$ What is the domain? (b) Complete the table. Are the values of y different than you expected? Explain. (c) Find the limit of y as x approaches 25 from the right and interpret its meaning.