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• (ㄱ) $\displaystyle \lim _ {h \rightarrow 0} {\frac{e ^ {h} -1} {h}} =1$ (ㄴ) $\displaystyle e= \lim _ {n \rightarrow \infty} {\left (1+ \frac{1} {n} \right) ^ {n}}$
• (ㄷ) $\displaystyle e= \lim _ {n \rightarrow \infty} {\left (1- \frac{1} {n} \right) ^ {-n}}$ (ㄹ) $\displaystyle e= \lim _ {x \rightarrow 1} {x ^ {\frac{1} {x-1}}}$
• (ㅁ) $\displaystyle e= \lim _ {x \rightarrow 0} {\left (1+x \right) ^ {1/x}}$ (ㅂ) $\displaystyle e= \sum _ {k=0} ^ {\infty} \frac{1} {k!}$