91Ó°ÊÓ

You will find a graphing calculator useful for Exercise. Let \(h(x)=\left(x^{2}-2 x-3\right) /\left(x^{2}-4 x+3\right)\) a. Make a table of the values of \(h\) at \(x=2.9,2.99,2.999,\) and so on. Then estimate \(\lim _{x \rightarrow 3} h(x) .\) What estimate do you arrive at if you evaluate \(h\) at \(x=3.1,3.01,3.001, \ldots\) instead? b. Support your conclusions in part (a) by graphing \(h\) near \(c=3\) and using Zoom and Trace to estimate \(y\) -values on the graph as \(x \rightarrow 3.\) c. Find \(\lim _{x \rightarrow 3} h(x)\) algebraically.

How many horizontal asymptotes can the graph of a given rational function have? Give reasons for your answer.

Use formal definitions to prove the limit statements. $$\lim _{x \rightarrow 0} \frac{-1}{x^{2}}=-\infty$$

Graph the rational functions .Include the graphs and equations of the asymptotes. $$y=\frac{x^{2}+1}{x-1}$$