Genel fonksiyonlarda limit hesaplamak için bazı pratik kurallar verilmiştir. Formüllerdeki a ve b sayılarının x'e göre sabit olduğu düşünülecektir
Genel fonksiyonlar için limit kuralları
![{\displaystyle {\mbox{Eger }}\lim _{x\to c}f(x)=L_{1}{\mbox{ ve }}\lim _{x\to c}g(x)=L_{2}{\mbox{ ise, o zaman:}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed8fff6ba876a7491bf7d171dd8b2825f32b74f6)
![{\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)
![{\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}={\frac {L_{1}}{L_{2}}}\qquad {\mbox{ eger }}L_{2}\neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/560e88ae23e742063ca073f08a78c5d187553cef)
![{\displaystyle \lim _{x\to c}\,f(x)^{n}=L_{1}^{n}\qquad {\mbox{ eger }}n{\mbox{ }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43582300d5006b8309a15a094bc28e52b2e6a5f0)
![{\displaystyle \lim _{x\to c}\,f(x)^{1 \over n}=L_{1}^{1 \over n}\qquad {\mbox{ eger }}n{\mbox{ bir pozitif tamsayi ise, ve eger }}n{\mbox{ cift sayi ise, o zaman }}L_{1}>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec33f0d4544cee22d83b8df6f54f48ccaf613c5a)
(L'Hôpital kuralı)
Basit fonksiyonlar
![{\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)
![{\displaystyle \lim _{x\to c}x^{r}=c^{r}\qquad {\mbox{ eger }}r{\mbox{ bir pozitif tam sayıdır}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a730b2c3dbda6194dd2220612bfd72fe59523ef)
![{\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{ eger }}r{\mbox{ tek sayı ise }}\\+\infty ,&{\mbox{ eger }}r{\mbox{ cift sayı ise}}\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dded8079c5d87b55a853ceae43792b94a2e7b826)
Logaritmik ve üstel fonksiyonlar
![{\displaystyle a>1{\mbox{ İçin}}:}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02d93830ce28ff2724f0bf863029d98936413186)
![{\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)
Trigonometrik fonksiyonlar
![{\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 a}\sin x=\sin a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04bf4a31eeee313433f14413d9e3c441d69576a9)
![{\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 a}\cos x=\cos a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/233fccfb3bbfdad201662ecc5dce951fd4baf7b9)
![{\displaystyle \lim _{x\to n^{\pm }}\tan(\pi x+{\frac {\pi }{2}})=\mp \infty \qquad {\mbox{ n : herhangi bir tamsayi }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4abebfb99fb811c04f75162ac49058df8e26de58)
Sonsuzluk yakınsamaları
![{\displaystyle \lim _{x\to \infty }N/x=0{\mbox{ herhangi bir reel N icin}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1336c7e935c2e1f0ea81a88d513eb1356f4121)
![{\displaystyle \lim _{x\to \infty }x/N={\begin{cases}\infty ,&N>0\\{\mbox{mevcut degildir}},&N=0\\-\infty ,&N<0\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e019c0f0b02fb8af2cca6bcc64869b12c9b5edc)
![{\displaystyle \lim _{x\to \infty }x^{N}={\begin{cases}\infty ,&N>0\\1,&N=0\\0,&N<0\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d65f9d24a6d8cf90b0d955281e7ad9c6f78a182a)
![{\displaystyle \lim _{x\to \infty }N^{x}={\begin{cases}\infty ,&N>1\\1,&N=1\\0,&N<1\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42a2b6999fd69fb03d41a14102bebf91d30927f4)
![{\displaystyle \lim _{x\to \infty }N^{-x}=\lim _{x\to \infty }1/N^{x}=0{\mbox{ herhangi bir N }}>1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b713c796b687c0b2109978207e853986dbe7277d)
![{\displaystyle \lim _{x\to \infty }{\sqrt[{x}]{N}}={\begin{cases}1,&N>0\\0,&N=0\\{\mbox{mevcut degildir}},&N<0\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a933c98a5d485eeff4f8f36be5fc51fc015f17c)
![{\displaystyle \lim _{x\to \infty }{\sqrt[{N}]{x}}=\infty {\mbox{ Herhangi bir N }}>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efd8873603dc543fd80f779c1e30ace6b92a18c5)
![{\displaystyle \lim _{x\to \infty }\log x=\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/40a3dc39adf241c3465eb63b5e002296b7d0c57e)
![{\displaystyle \lim _{x\to 0^{+}}\log x=-\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb7a454bbcf3fafcf6ea82fdcd1b8346c5c0d1a7)