91Ó°ÊÓ

In Exercises \(1-6,\) find the average rate of change of the function over each interval. \(f(x)=x^{3}+1\) (a) $$[2,3] \quad$$ \((b)\lceil- 1,1]\)

In Exercises \(1-10,\) find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. $$y=\frac{1}{(x+2)^{2}}$$

In Exercises \(1-8,\) use graphs and tables to find (a) \(\lim _{x \rightarrow \infty} f(x)\) and (b) \(\lim _{x \rightarrow-\infty} f(x)\) (c) Identify all horizontal asymptotes. $$f(x)=\cos \left(\frac{1}{x}\right)$$

In Exercises \(1 - 4 ,\) an object dropped from rest from the top of a tall building falls \(y = 16 t ^ { 2 }\) feet in the first \(t\) seconds. Find the average speed during the first 3 seconds of fall.

In Exercises \(1-10,\) find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. $$y=\frac{x+1}{x^{2}-4 x+3}$$

In Exercises \(1 - 4 ,\) an object dropped from rest from the top of a tall building falls \(y = 16 t ^ { 2 }\) feet in the first \(t\) seconds. Find the average speed during the first 4 seconds of fall.

In Exercises \(1-6,\) find the average rate of change of the function over each interval. \(f(x)=\sqrt{4 x+1}\) (a) $$[0,2] \quad$$ (b) $$[10,12]$$

In Exercises \(1-8,\) use graphs and tables to find (a) \(\lim _{x \rightarrow \infty} f(x)\) and (b) \(\lim _{x \rightarrow-\infty} f(x)\) (c) Identify all horizontal asymptotes. $$f(x)=\frac{\sin 2 x}{x}$$

In Exercises \(1-6,\) find the average rate of change of the function over each interval. \(f(x)=e^{x}\) (a) $$[-2,0] \quad$$ (b) $$[1,3]$$

In Exercises \(1-10,\) find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. $$y=\frac{1}{x^{2}+1}$$