تیۆرمی دوو مەرج

${\displaystyle g(x)\leq f(x)\leq h(x)\,}$

${\displaystyle \lim _{x\to a}g(x)=\lim _{x\to a}h(x)=L.\,}$

${\displaystyle \lim _{x\to a}f(x)=L.}$

${\displaystyle L=\lim _{x\to a}g(x)\leq \liminf _{x\to a}f(x)\leq \limsup _{x\to a}f(x)\leq \lim _{x\to a}h(x)=L,}$

${\displaystyle L\leq \liminf _{x\to a}f(x)\leq \limsup _{x\to a}f(x)\leq L,}$

${\displaystyle \lim _{x\to a}(f(x)\cdot g(x))=\lim _{x\to a}f(x)\cdot \lim _{x\to a}g(x),}$

${\displaystyle -1\leq \sin({\tfrac {1}{x})\leq 1.\,}$

${\displaystyle -x^{2}\leq x^{2}\sin({\tfrac {1}{x})\leq x^{2}\,}$

${\displaystyle \lim _{x\to 0}-x^{2}=\lim _{x\to 0}x^{2}=0}$،

${\displaystyle {\begin{aligned}&\lim _{x\to 0}{\frac {\sin x}{x}=1,\\[10pt]&\lim _{x\to 0}{\frac {1-\cos x}{x}=0.\end{aligned}$