• ${\displaystyle \lim _{x\to \infty }(1+{\frac {1}{x}})^{x}=e}$  
• ${\displaystyle \lim _{x\to 0}(1+x)^{\frac {k}{x}}=e^{k}(k=1:x)}$  
• ${\displaystyle \lim _{x\to 0}\cos(x)=1}$  
• ${\displaystyle \lim _{x\to 0}{\frac {\tan(x)}{x}}=1}$  

${\displaystyle \lim _{n\to \infty }(a_{n}+b_{n})=\lim _{n\to \infty }a_{n}+\lim _{n\to \infty }b_{n}.}$  

${\displaystyle \lim _{n\to \infty }(a_{n}-b_{n})=\lim _{n\to \infty }a_{n}-\lim _{n\to \infty }b_{n}.}$  

${\displaystyle \lim _{n\to \infty }(a_{n}.b_{n})=\lim _{n\to \infty }a_{n}.\lim _{n\to \infty }b_{n}.}$  

${\displaystyle \lim _{n\to \infty }{\frac {a_{n}}{b_{n}}}={\frac {\lim _{n\to \infty }a_{n}}{\lim _{n\to \infty }b_{n}}}.}$  

b_n ≠ 0 və ${\displaystyle \lim _{n\to \infty }b_{n}}$   ≠ 0.

${\displaystyle \lim _{n\to \infty }ca_{n}=c\lim _{n\to \infty }a_{n}}$   c = const.

${\displaystyle \lim _{n\to \infty }(c_{1}a_{n}+c_{2}b_{n})=c_{1}\lim _{n\to \infty }a_{n}+c_{2}\lim _{n\to \infty }b_{n}}$  

с₁ = const, c₂ = const.

${\displaystyle \lim _{n\to \infty }\log _{b}a_{n}=log_{b}a}$   b > 0, a > 0, b ≠ 1 şərtilə.

${\displaystyle \lim _{n\to \infty }{a_{n}}^{p}=a^{p}}$   а > 0 p olduqda