(C) $\lim _{x \rightarrow 0^{+}}\left( e ^x+x\right)^{1 / x}$ If $\lim _{x \rightarrow a } f (x)=1$ and $\lim _{x \rightarrow a } g (x)=\infty$, then $\lim _{x \rightarrow a }[ f (x)]^{ g (x)}= e ^{\lim _{x \rightarrow a } g (x)[ f (x)-1]}$ $=e^{\lim _{x \rightarrow 0^{+}}\left(\frac{e^x-1+x}{x}\right)}$ $= e ^{\lim _{x \rightarrow 0^{+}}\left(1+\frac{ e ^x-1}{x}\right)}$ $= e ^{1+1}$ $= e ^2$
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