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

The limit as e^{e^x} approaches 0+of (e^{e^x-2})/(e^{e^x)} is 1/(e^2)

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

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

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

Decimal Notation

0.13533 \dots

Solution steps

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}}

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What is the limit as e^{e^x} approaches 0+of (e^{e^x-2})/(e^{e^x)} ?
The limit as e^{e^x} approaches 0+of (e^{e^x-2})/(e^{e^x)} is 1/(e^2)