91Ó°ÊÓ

Find the derivative of the function. \(f(x)=5\)

Horizontal Asymptotes and Limits at Infinity In Exercises \(29 - 34 ,\) use a graphing utility to graph the function and verify that the horizontal asymptote corresponds to the limit at infinity. $$ y = \frac { 3 x } { 1 - x } $$

Approximating a Limit Graphically, use a graphing utility to graph the function and approximate the limit accurate to three decimal places. $$ \lim _{x \rightarrow 0} \frac{\sin 2 x}{x} $$

Horizontal Asymptotes and Limits at Infinity In Exercises \(29 - 34 ,\) use a graphing utility to graph the function and verify that the horizontal asymptote corresponds to the limit at infinity. $$ y = \frac { x ^ { 2 } } { x ^ { 2 } + 4 } $$

Approximating a Limit Graphically, use a graphing utility to graph the function and approximate the limit accurate to three decimal places. $$ \lim _{x \rightarrow 0} \frac{1-\cos 2 x}{x} $$

Find the derivative of the function. \(f(x)=-1\)

Approximating a Limit Graphically, use a graphing utility to graph the function and approximate the limit accurate to three decimal places. $$ \lim _{x \rightarrow 1} \frac{1-\sqrt[3]{x}}{1-x} $$

Horizontal Asymptotes and Limits at Infinity In Exercises \(29 - 34 ,\) use a graphing utility to graph the function and verify that the horizontal asymptote corresponds to the limit at infinity. $$ y = \frac { 5 x } { 1 - x ^ { 2 } } $$

Finding the Area of a Region,complete the table to show the approximate area of the region bounded by the graph of \(f\) and the \(x\) -axis over the specified interval using the indicated numbers \(n\) of rectangles of equal width. Then find the exact area as \(n \rightarrow \infty\). $$\begin{array}{ll}{\text { Function }} & {\text { Interval }} \\ {f(x)=2 x+5} & {[0,4]}\end{array}$$

Find the derivative of the function. \(g(x)=9-\frac{1}{3} x\)