Fundamental exponential limits for JEE

Formula

\[\lim_{x\to \infty}\left(1+\frac1x\right)^x=e,\qquad \lim_{x\to 0}(1+x)^{1/x}=e\]

Variables: \(e\) is Euler's number.

Conditions: Second limit uses \(1+x>0\) near \(0\).

Evaluating indeterminate forms of type \(1^\infty\).