91Ó°ÊÓ

Determine the interval(s) on which the following functions are continuous. Be sure to consider right- and left-continuity at the endpoints. $$f(x)=(2 x-3)^{2 / 3}$$

We write \(\lim _{x \rightarrow a^{+}} f(x)=-\infty\) if for any negative number \(N\) there exists \(\delta>0\) such that $$f(x)

\(A\) function \(f\) is even if \(f(-x)=f(x)\) for all \(x\) in the domain of \(f\). Suppose \(f\) is even. with \(\lim _{x \rightarrow 2^{+}} f(x)=5\) and \(\lim _{x \rightarrow 2^{-}} f(x)=8 .\) Evaluate the following limits. a. \(\lim _{x \rightarrow-2^{+}} f(x)\) b. \(\lim _{x \rightarrow-2^{-}} f(x)\)

Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. $$f(x)=-3 e^{-x}$$

Use analytical methods and/or a graphing utility en identify the vertical asymptotes (if any) of the following functions. $$f(x)=\frac{x^{2}-3 x+2}{x^{10}-x^{9}}$$

Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. $$f(x)=2^{x}$$

Evaluate the following limits, where a and \(b\) are fixed real numbers. \(\lim _{h \rightarrow 0} \frac{\frac{1}{5+h}-\frac{1}{5}}{h}\)

Use analytical methods and/or a graphing utility en identify the vertical asymptotes (if any) of the following functions. $$g(x)=2-\ln x^{2}$$

Determine the interval(s) on which the following functions are continuous. Be sure to consider right- and left-continuity at the endpoints. $$f(z)=(z-1)^{3 / 4}$$

A function \(g\) is odd if \(g(-x)=-g(x)\) for all \(x\) in the domain of \(g\). Suppose \(g\) is odd, with \(\lim _{x \rightarrow 2^{+}} g(x)=5\) and \(\lim _{x \rightarrow 2^{-}} g(x)=8 .\) Evaluate the following limits. a. \(\lim _{x \rightarrow-2^{+}} g(x)\) b. \(\lim _{x \rightarrow-2^{-}} g(x)\)