ខាងក្រោមនេះជាតារាងលីមីតអនុគមន៍ទូទៅ។ កត់សំគាល់ថា a និងb ជាចំនួនថេរតាមអថេរ x ។
លីមីតនៃអនុគមន៍ទូទៅ[កែប្រែ]
- ប្រសិនបើ
និង
នោះគេបាន
![{\displaystyle \lim _{x\to c}\,[f(x)\pm g(x)]=L_{1}\pm L_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cb00a9174f995bae626da947886d0229d14b275)
![{\displaystyle \lim _{x\to c}\,[f(x)g(x)]=L_{1}\times L_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d8693d558a7dfc0f5f0c5900a05dd950f6f7f1)
ប្រសិនបើ ![{\displaystyle L_{2}\neq 0\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/172f9cdb147dad1ff907540c91fc6217172edce0)
ប្រសិនបើ n ជាចំនួនគត់វិជ្ជមាន
ប្រសិនបើ n ជាចំនួនគត់វិជ្ជមានគូ និង![{\displaystyle L_{1}>0\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e9943fb0f77c026bb5ab4255aa8750414a831b45)
ប្រសិនបើ
ឬ
(ច្បាប់ឡូពីតាល់)
លីមីតនៃអនុគមន៍សាមញ្ញ[កែប្រែ]
![{\displaystyle \lim _{x\to c}a=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f4aaff459f69192f8dc759314582c6751a41363)
![{\displaystyle \lim _{x\to c}x=c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/337e2c532e2cedd5b0d67bd903d39cd1cbacaf77)
![{\displaystyle \lim _{x\to c}ax+b=ac+b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d30f7a105c48fca95512fc7752493eb7dfa6d29c)
ប្រសិនបើ r ជាចំនួនគត់វិជ្ជមាន
![{\displaystyle \lim _{x\to 0^{+}}{\frac {1}{x^{r}}}=+\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/97a337010a50e6173a4b1c1b5953ac7ed9ed4bab)
![{\displaystyle \lim _{x\to 0^{-}}{\frac {1}{x^{r}}}=\left\{{\begin{matrix}-\infty ,&{\mbox{if }}r{\mbox{ is odd}}\\+\infty ,&{\mbox{if }}r{\mbox{ is even}}\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60f6522416e7e41f86b8cbfa33c88d7ab673ecf2)
លីមីតនៃអនុគមន៍លោការីត និងអនុគមន៍អ៊ិចស្ប៉ូណង់ស្យែល[កែប្រែ]
- ចំពោះ
![{\displaystyle a>1:\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e869775fd93e682129d0bb7e0c98158f06e3fee0)
![{\displaystyle \lim _{x\to 0^{+}}\log _{a}x=-\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/72808181c55d9096253749e5968f71c47c87bd9b)
![{\displaystyle \lim _{x\to \infty }\log _{a}x=\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/bac08a36cc877e299461440d1c9c08d88373f041)
![{\displaystyle \lim _{x\to -\infty }a^{x}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5300504623b781a3067f7f6a88dfb5bf0ffb46f)
![{\displaystyle \lim _{x\to \infty }a^{x}=\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/44d6d9be2238a6b9a4c2de1ba6eb2a7430e1dee8)
លីមីតនៃអនុគមន៍ត្រីកោណមាត្រ[កែប្រែ]
![{\displaystyle \lim _{x\to a}\sin x=\sin a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04bf4a31eeee313433f14413d9e3c441d69576a9)
![{\displaystyle \lim _{x\to a}\cos x=\cos a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/233fccfb3bbfdad201662ecc5dce951fd4baf7b9)
![{\displaystyle \lim _{x\to 0}{\frac {\sin x}{x}}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f2fb52f5211c7b7aa69d9e75195afaab5b9d5b1)
![{\displaystyle \lim _{x\to 0}{\frac {1-\cos x}{x}}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e68c22c5c70aa65f792c06b2cf2fb6e1ecfe16b)
![{\displaystyle \lim _{x\to 0}{\frac {1-\cos x}{x^{2}}}={\frac {1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/580636aba444eda89b876cfc9e36e1f31d40e771)
ចំពោះគ្រប់ចំនួនគត់ n
លីមីត x ខិតទៅរកអនន្ត[កែប្រែ]
ចំពោះគ្រប់ចំនួនពិត N
![{\displaystyle \lim _{x\to \infty }x/N={\begin{cases}\infty ,&N>0\\{\mbox{does not exist}},&N=0\\-\infty ,&N<0\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a8f8a2be92a1a015d2cc0060d5c5dfc77960711)
ចំពោះ
![{\displaystyle \lim _{x\to 0^{+}}\log x=-\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb7a454bbcf3fafcf6ea82fdcd1b8346c5c0d1a7)
![{\displaystyle \lim _{x\to 3}x^{2}=9}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3acd9a42c04db99e7cdb5965ba85c415d895ba18)
![{\displaystyle \lim _{x\to 0+}x^{x}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61ca3073092152fd0d7f87d9675ae90d77adadd6)
![{\displaystyle \lim _{x\to \infty }{\frac {1}{x}}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2306e1c19001b78c23333e9d8d54501b77d54f9d)
![{\displaystyle \lim _{x\to 0}{\frac {\sin {x}}{x}}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0355a0c4733c85a38b2e2837a1c9133ccad00c)
![{\displaystyle \lim _{x\to 0}\cos(cx)^{2/x^{2}}=e^{-c^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/155f407785c2796041dcfa063561ed4694be9613)
![{\displaystyle \lim _{n\to \infty }2^{1/n}=\lim _{n\to \infty }{\sqrt[{n}]{2}}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9ed1853400cf1640107c84a627ef2a6cc03b045)
![{\displaystyle \lim _{n\to \infty }n^{1/n}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c562733a14872bac2d27b958465aab436c2b9dde)
![{\displaystyle \lim _{n\to \infty }{\frac {2^{n}}{n!}}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/17fe999bf23dd9ec9a443ac6ac567244637091a8)
![{\displaystyle \lim _{n\to \infty }\left(1+{\frac {x}{n}}\right)^{n}=e^{x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8d2337d253d80e6a59760b1afd15c799205e2e2)