Problem 16
Find the limit. $$ \lim _{x \rightarrow 0} e^{-x} \sin \pi x $$
Problem 16
In Exercises \(7-20,\) find the vertical asymptotes (if any) of the function. $$ f(z)=\ln \left(z^{2}-4\right) $$
Problem 16
Use the Horizontal Line Test to determine whether the function is one-to-one on its entire domain and therefore has an inverse function. To print an enlarged copy of the graph, go to the website www.mathgraphs.com. $$ f(x)=\frac{x^{2}}{x^{2}+4} $$
Problem 17
In Exercises \(7-20,\) find the vertical asymptotes (if any) of the function. $$ f(x)=\frac{1}{e^{x}-1} $$
Problem 17
Find the domain of the function. $$ f(x)=\sqrt{x}+\sqrt{1-x} $$
Problem 17
Find an equation of the line that passes through the point and has the indicated slope. Sketch the line. $$ (3,-2) \quad m=3 $$
Problem 17
Sketch the graph of the function. $$ f(x)=3^{-x^{2}} $$
Problem 17
In Exercises \(17-20\), use a graphing utility to graph the function. Determine whether the function is one-to-one on its entire domain. $$ h(s)=\frac{1}{s-2}-3 $$
Problem 17
Discuss the continuity of each function. $$ f(x)=\frac{x^{2}-1}{x+1} $$
Problem 17
Find the limits. \(f(x)=5-x, g(x)=x^{3}\) (a) \(\lim _{x \rightarrow 1} f(x)\) (b) \(\lim _{x \rightarrow 4} g(x)\) (c) \(\lim _{x \rightarrow 1} g(f(x))\)
