$\displaystyle \large \lim_{x \,\to\, \infty}{\normalsize {\Big(1+\dfrac{1}{x}\Big)}^{\displaystyle x}}$ $\,=\,$ $e$

The limit of $1+\dfrac{1}{x}$ raised to the power of $x$ as $x$ approaches infinity is equal to mathematical constant $e$.

In limits, the exponential functions similar to this function are often appeared. So, it’s considered as a standard result and used as a formula in calculus for evaluating the limits of exponential functions when its input tends to infinity.

This standard result of limits can also be written in terms of any variable.

$(1) \,\,\,$ $\displaystyle \large \lim_{g \,\to\, \infty}{\normalsize {\Big(1+\dfrac{1}{g}\Big)}^{\displaystyle g}}$ $\,=\,$ $e$

$(2) \,\,\,$ $\displaystyle \large \lim_{y \,\to\, \infty}{\normalsize {\Big(1+\dfrac{1}{y}\Big)}^{\displaystyle y}}$ $\,=\,$ $e$

Learn how to prove the limit of $x$-th power of binomial $1+\dfrac{1}{x}$ as $x$ approaches infinity is equal to $e$ in mathematics.

Latest Math Topics

Mar 21, 2023

Feb 25, 2023

Feb 17, 2023

Feb 10, 2023

Jan 15, 2023

Latest Math Problems

Mar 03, 2023

Mar 01, 2023

Feb 27, 2023

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved