#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

$$
\frac {1} {\ln e}
$$

$$
1
$$