지수함수 극한

[출제의도] 지수함수의 극한을 구할 수 있는가? $\displaystyle \lim\limits _{x\rightarrow 0} \frac{e ^{2x} + e ^{3x} - 2}{2 x}$$\displaystyle = \lim\limits _{x\rightarrow 0} \frac{\left( e ^{2x} - 1 \right) + \left( e ^{3x} - 1 \right)}{2 x}$ $\displaystyle = \lim\limits _{x \rightarrow 0} {} \frac{e ^{2 x} - 1}{2 x} + \lim\limits _{x \rightarrow 0} \frac{e ^{3 x} - 1}{2 x}$$\displaystyle = \lim\limits _{x \rightarrow 0} {} \frac{e ^{2 x} - 1}{2 x} + = \lim\limits _{x \rightarrow 0} {\left( \frac{e ^{2 x} - 1}{2 x} \times \frac{3}{2} \right)}$ $\displaystyle = 1 + 1 \times \frac{3}{2} = \frac{5}{2}$