Math Doubts

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

Fact-checked:

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.

Learn Proof
Ashok Kumar B.E. - Founder of Math Doubts

Ashok Kumar, B.E.

Founder of Math Doubts

A Specialist in Mathematics, Physics, and Engineering with 14 years of experience helping students master complex concepts from basics to advanced levels with clarity and precision.

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