Limit (riyaziyyat)

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

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

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

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

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

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

• Mathwords: Limit