Problem 24
In Exercises \(21-26,\) find \(\lim _{x \rightarrow \infty} y\) and \(\lim _{x \rightarrow-\infty} y\). $$y=\frac{2 x+\sin x}{x}$$
Problem 24
Rocket Launch At \(t\) sec after lift-off, the height of a rocket is 3\(t^{2}\) ft. How fast is the rocket climbing after 10 \(\mathrm{sec} ?\)
Problem 24
In Exercises \(19 - 28 ,\) determine the limit graphically. Confirm algebraically. $$\lim _ { x \rightarrow 0 } \frac { \sin 2 x } { x }$$
Problem 25
In Exercises \(19 - 28 ,\) determine the limit graphically. Confirm algebraically. $$\lim _ { x \rightarrow 0 } \frac { \sin x } { 2 x ^ { 2 } - x }$$
Problem 25
In Exercises \(21-26,\) find \(\lim _{x \rightarrow \infty} y\) and \(\lim _{x \rightarrow-\infty} y\). $$y=\frac{\sin x}{2 x^{2}+x}$$
Problem 25
Area of Circle What is the rate of change of the area of a circle with respect to the radius when the radius is \(r=3\) in. ?
Problem 26
In Exercises \(19 - 28 ,\) determine the limit graphically. Confirm algebraically. $$\lim _ { x \rightarrow 0 } \frac { x + \sin x } { x }$$
Problem 26
In Exercises \(21-26,\) find \(\lim _{x \rightarrow \infty} y\) and \(\lim _{x \rightarrow-\infty} y\). $$y=\frac{x \sin x+2 \sin x}{2 x^{2}}$$
Problem 26
Volume of Sphere What is the rate of change of the volume of a sphere with respect to the radius when the radius is \(r=2\) in.?
Problem 27
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. $$f(x)=\frac{1}{x^{2}-4}$$
