Generalized exponential limit for JEE

Formula

\[\lim_{x\to \infty}\left(1+\frac{a}{x}\right)^x=e^a,\qquad \lim_{x\to 0}(1+ax)^{1/x}=e^a\]

Variables: \(a\in\mathbb R\).

Conditions: For second form, \(1+ax>0\) near the limit point.

Indeterminate forms and sequence/function limits.