91Ó°ÊÓ

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$ \left(\frac{1}{2}, 1\right),\left(-\frac{3}{2},-5\right) $$

Complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. \(\lim _{x \rightarrow 0} \frac{\sqrt{x+1}-1}{x}\) \(\begin{array}{|c|c|c|c|c|c|c|}\hline x & {-0.1} & {-0.01} & {-0.001} & {0} & {0.001} & {0.01} & {0.1} \\ \hline f(x) & {} & {} & {?} & {} & {} \\\ \hline\end{array}\)

Determine whether the function is continuous on the entire real line. Explain your reasoning. $$ f(x)=\frac{3 x}{x^{2}+1} $$

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$ \left(\frac{2}{3},-\frac{1}{3}\right),\left(\frac{5}{6}, 1\right) $$

Plot the points and find the slope of the line passing through the pair of points. $$ (-2,0),(1,4) $$

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$ (2,2),(4,14) $$

Determine whether the function is continuous on the entire real line. Explain your reasoning. $$ f(x)=\frac{2 x-1}{x^{2}-8 x+15} $$

decide whether the equation defines \(y\) as a function of \(x .\) $$ y=|x+2| $$

Complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. \(\lim _{x \rightarrow 0^{-}} \frac{\frac{1}{x+4}-\frac{1}{4}}{x}\) \(\begin{array}{|c|c|c|c|c|c|}\hline x & {-0.5} & {-0.1} & {-0.01} & {-0.001} & {0} \\ \hline f(x) & {} & {} & {} & {?} \\ \hline\end{array}\)

Plot the points and find the slope of the line passing through the pair of points. $$ (3,-4),(5,2) $$