public-notes/Another Way to Define e.md

#Math #Calculus

Limit to solve:

\lim _{x\to 0} \frac {e^x-1} {x}

Let t = e^x - 1

\lim _{t\to 0} \frac {t} {\ln(t+1)}

\lim _{t\to 0} \frac {1} {\frac {1} {t} \ln(1+t)}

Inverse power log rule

\lim _{t\to 0} \frac {1} {\ln(1+t)^{\frac {1} {t}}}

Definition of e

\frac {1} {\ln e}

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