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Another Way to Define e.md

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