# Limits rules at infinity

### Algebraic functions

$\displaystyle \large \lim_{x\,\to\,\pm\infty}{\normalsize \dfrac{1}{x}}$ $\,=\,$ $0$

### Exponential functions

$\displaystyle \large \lim_{x\,\to\,+\infty}{\normalsize e^x}$ $\,=\,$ $\infty$

$\displaystyle \large \lim_{x\,\to\,-\infty}{\normalsize e^x}$ $\,=\,$ $0$

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

### Trigonometric functions

$\displaystyle \large \lim_{x\,\to\,\pm \infty}{\normalsize \dfrac{\sin{x}}{x}}$ $\,=\,$ $0$

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

###### Maths Topics

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

###### Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.