logowanie

Działania na granicach funkcji

Jeżeli ${\displaystyle \underset{x\to x_0}{\lim }f\left(x\right)=a}$ i ${\displaystyle \underset{x\to x_0}{\lim }g\left(x\right)=b}$, to:

${\displaystyle \underset{x\to x_0}{\lim }\left(f\right(x)+g(x\left)\right)=a+b}$,
${\displaystyle \underset{x\to x_0}{\lim }\left(f\right(x)-g(x\left)\right)=a-b}$,
${\displaystyle \underset{x\to x_0}{\lim }\left(f\right(x\left)g\right(x\left)\right)=ab}$,
${\displaystyle b\ne 0\Rightarrow \underset{x\to x_0}{\lim }\frac{f\left(x\right)}{g\left(x\right)}=\frac{a}{b}}$.

Jeżeli jedna z funkcji jest stała, np. f(x) = c, wtedy mamy
${\displaystyle \underset{x\to x_0}{\lim }\left(f\right(x\left)g\right(x\left)\right)=\underset{x\to x_0}{\lim }cg\left(x\right)=c\underset{x\to x_0}{\lim }g\left(x\right)}$,

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