$\displaystyle \large \lim_{x \,\to\, 0} \, {\normalsize (1+x)^{\Large \frac{1}{x}}}$ Rule

Formula

$\displaystyle \large \lim_{x \,\to\, 0} \, {\normalsize (1+x)^{\Large \frac{1}{x}}}$ $\,=\,$ $\large e$

Introduction

Limit of $(1+x)^\frac{1}{x}$ when $x$ tends to $0$

Proof

Learn how to derive a limit rule for finding the limit of an exponential function ${(1+x)}^{\frac{1}{x}}$ as $x$ approaches zero by using Binomial Theorem.