This is a list of limits for common functions. Note that a and b are constants with respect to x.
Limits for general functions[edit | edit source]
If
and
then:
![{\displaystyle \lim _{x\to c}{\Big [}f(x)\pm g(x){\Big ]}=L_{1}\pm L_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b49f252a1ed76f8b15d6b189242aa9462cceb52b)
![{\displaystyle \lim _{x\to c}{\Big [}f(x)\cdot g(x){\Big ]}=L_{1}\cdot L_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f113af2b526910d5ad3c2c6b6142f7bd63f7d25f)


![{\displaystyle \lim _{x\to c}{\sqrt[{n}]{f(x)}}={\sqrt[{n}]{L_{1}}}\qquad {\text{ if }}n{\text{ is a positive integer, and if }}n{\text{ is even, then }}L_{1}>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/241e28dad0665547cf53d756727f851e1380a4a7)
(L'Hôpital's rule)
Limits of general functions[edit | edit source]






![{\displaystyle \lim _{n\to \infty }{\frac {n}{\sqrt[{n}]{n!}}}=e}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e67d9f7e2588c9b3d418f1107e9ea27b8f330ed)







Logarithmic and exponential functions[edit | edit source]
For
:















![{\displaystyle \lim _{x\to \infty }{\sqrt[{x}]{N}}={\begin{cases}1,&N>0\\0,&N=0\\{\text{does not exist}},&N<0\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61204dd0899445181689dd595b467af963c3150e)
![{\displaystyle \lim _{x\to \infty }{\sqrt[{N}]{x}}=\infty {\text{ for any }}N>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b3529665ba00830f3f5a8e5160afe35d422924f5)


- List_of_limits