Textbook Problem

Indeterminate Forms Show that the indeterminate forms 0°, ∞°, and 1^∞ do not always have a value of 1 by evaluating each limit.

$\begin{array}{l}(\text{a})\underset{x\to 0^{+}}{\lim }{x}^{\ln 2/\left(1+\ln x\right)}\hfill \\ (\text{b})\underset{x\to \infty }{\lim }{x}^{\ln 2/\left(1+\ln x\right)}\hfill \\ (\text{c})\underset{x\to 0}{\lim }{\left(x+1\right)}^{\left(\ln 2\right)/x}\hfill \end{array}$