limit as e^{e^x} approaches 0+of (e^{e^x-2})/(e^{e^x)}

解

e^{e^{e^{e^{x}}}} \to 0 + lim \frac{e ^{e^{e^{e^{x}}} - 2}}{e ^{e^{e^{e^{x}}}}}

\frac{1}{e ^{2}}

十進法表記

0.13533 \dots

解答ステップ

e^{e^{e^{e^{x}}}} \to 0 + lim \frac{e ^{e^{e^{e^{x}}} - 2}}{e ^{e^{e^{e^{x}}}}}

\frac{e ^{e^{e^{e^{x}}} - 2}}{e ^{e^{e^{e^{x}}}}} = \frac{1}{e ^{2}}

= e^{e^{e^{e^{x}}}} \to 0 + lim (\frac{1}{e ^{2}})

x \to a lim c = c

= \frac{1}{e ^{2}}