지수함수 극한

[출제의도] 지수함수의 극한값을 구한다. $\displaystyle \lim\limits _{x \rightarrow 0} {} \frac{f ( x )}{x}$$\displaystyle = \lim\limits _{x \rightarrow 0} {} \frac{e ^{x} - e ^{\mathit{-} x}}{x}$ $\displaystyle = \lim\limits _{x \rightarrow 0} {} \frac{e ^{x} - 1 + 1 - e ^{\mathit{-} x}}{x}$ $\displaystyle = \lim\limits _{x \rightarrow 0} {} \left( \frac{e ^{x} - 1}{x} + \frac{e ^{\mathit{-} x} - 1}{\mathit{-} x} \right)$ 이때 $\displaystyle \lim\limits _{x \rightarrow 0} {} \frac{e ^{x} - 1}{x}$$= 1$, $\displaystyle \lim\limits _{x \rightarrow 0} {} \frac{e ^{\mathit{-} x} - 1}{\mathit{-} x}$$= 1$이므로 $\displaystyle \lim\limits _{x \rightarrow 0} \frac{f ( x )}{x}$$= 1 + 1$$= 2$