91Ó°ÊÓ

Indeterminate Forms Show that the indeterminate forms \(0^{0}, \infty^{0},\) and \(1^{\infty}\) do not always have a value of 1 by evaluating each limit. $$ (a) \lim _{x \rightarrow 0^{+}} x^{(\ln 2) /(1+\ln x)}$$ $$ (b) \lim _{x \rightarrow \infty^{+}} x^{(\ln 2) /(1+\ln x)}$$ $$ (c) \lim _{x \rightarrow 0}(x+1)^{(\ln 2) / x}$$

Asymptotes Compare the asymptotes of the natural exponentitul function with those of the natural logarithmic function.

Probability The median waiting time (in minutes) for people waiting for service in a convenience store is given by the solution of the equation \(\int_{0}^{x} 0.3 e^{-0.3 t} d t=\frac{1}{2}\) What is the median waiting time?