91Ó°ÊÓ

In Exercises \(19 - 28 ,\) determine the limit graphically. Confirm algebraically. $$\lim _ { x \rightarrow 0 } \frac { \sin ^ { 2 } x } { x }$$

In Exercises \(19 - 28 ,\) determine the limit graphically. Confirm algebraically. $$\lim _ { x \rightarrow 0 } \frac { 3 \sin 4 x } { \sin 3 x }$$

In Exercises \(27-34,\) (a) find the vertical asymptotes of the graph of \(f(x) .(\) b) Describe the behavior of \(f(x)\) to the left and right of each vertical asymptote. $$f(x)=\frac{x^{2}-1}{2 x+4}$$

Horizontal Tangent At what point is the tangent to \(f(x)=x^{2}+4 x-1\) horizontal?

In Exercises \(27-34,\) (a) find the vertical asymptotes of the graph of \(f(x) .(\) b) Describe the behavior of \(f(x)\) to the left and right of each vertical asymptote. $$f(x)=\frac{x^{2}-2 x}{x+1}$$

In Exercises 29 and 30 , use a graph to show that the limit does not exist. $$\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } - 4 } { x - 1 }$$

In Exercises 29 and 30 , use a graph to show that the limit does not exist. $$\lim _ { x \rightarrow 2 } \frac { x + 1 } { x ^ { 2 } - 4 }$$

Horizontal Tangent At what point is the tangent to \(f(x)=3-4 x-x^{2}\) horizontal?

In Exercises \(27-34,\) (a) find the vertical asymptotes of the graph of \(f(x) .(\) b) Describe the behavior of \(f(x)\) to the left and right of each vertical asymptote. $$f(x)=\frac{1-x}{2 x^{2}-5 x-3}$$

Finding Tangents and Normals (a) Find an equation for each tangent to the curve \(y=1 /(x-1)\) that has slope \(-1 .\) (See Exercise \(21 )\) (b) Find an equation for each normal to the curve \(y=1 /(x-1)\)that has slope 1