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

The limit as e^{e^x} approaches 0 of ((e^x)^{-2})/(e^x) is 1/(e^{3e^{e^x)}}

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

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

\frac{1}{e ^{3 e^{e^{x}}}}

Solution steps

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

x \to a lim c = c

= \frac{( e ^{e^{e^{x}}} ) ^{- 2}}{e ^{e^{e^{x}}}}

Simplify

\frac{( e ^{e^{e^{x}}} ) ^{- 2}}{e ^{e^{e^{x}}}} : \frac{1}{e ^{3 e^{e^{x}}}}

= \frac{1}{e ^{3 e^{e^{x}}}}

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What is the limit as e^{e^x} approaches 0 of ((e^x)^{-2})/(e^x) ?
The limit as e^{e^x} approaches 0 of ((e^x)^{-2})/(e^x) is 1/(e^{3e^{e^x)}}