91Ó°ÊÓ

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. $$f(x)=\frac{e^{-x}}{x}$$

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

In Exercises \(1-10,\) find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. $$y=|x-1|$$

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. $$f(x)=\frac{3 x^{3}-x+1}{x+3}$$

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 speed of the object at \(t = 4\) seconds and confirm your answer algebraically.

In Exercises \(1-6,\) find the average rate of change of the function over each interval. \(f(x)=\ln x\) (a) \([1,4], \quad\) ( b) \([100,103]\)

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

In Exercises \(1-6,\) find the average rate of change of the function over each interval. \(f(x)=\cot t\) (a) \([\pi / 4,3 \pi / 4] \quad\) (b) \([\pi / 6, \pi / 2]\)

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. $$f(x)=\frac{3 x+1}{|x|+2}$$

In Exercises 5 and \(6 ,\) use \(\lim _ { x \rightarrow c } k = k , \lim _ { x \rightarrow c } x = c ,\) and the properties of limits to find the limit. $$\lim _ { x \rightarrow c } \left( 2 x ^ { 3 } - 3 x ^ { 2 } + x - 1 \right)$$