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5 Reihen, Grenzwert und Stetigkeit

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5.2 Grenzwerte von Funktionen

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5.2.4 Rechenregeln für Grenzwerte

1.

$\underset{x\to x_0}{lim}C\cdot f\left(x\right)=C\cdot \underset{x\to x_0}{lim}f\left(x\right)$, wobei $C$ = konstant.

2.

$\underset{x\to x_0}{lim}\left[f\left(x\right)\pm g\left(x\right)\right]=\underset{x\to x_0}{lim}f\left(x\right)\pm \underset{x\to x_0}{lim}g\left(x\right)$

3.

$\underset{x\to x_0}{lim}\left[f\left(x\right)\cdot g\left(x\right)\right]=\underset{x\to x_0}{lim}f\left(x\right)\cdot \underset{x\to x_0}{lim}g\left(x\right)$

4.

$\underset{x\to x_0}{lim}\sqrt[n]{f\left(x\right)}=\sqrt[n]{\underset{x\to x_0}{lim}f\left(x\right)}$

5.

$\underset{x\to x_0}{lim}{\left(f\left(x\right)\right)}^n={\left(\underset{x\to x_0}{lim}f\left(x\right)\right)}^n$

6.

$\underset{x\to x_0}{lim}{a}^{f\left(x\right)}=a^{\underset{x\to x_0}{lim}f\left(x\right)}$

7.

$\underset{x\to x_0}{lim}\left[{log}_a\left(f\left(x\right)\right)\right]={log}_a\left(\underset{x\to x_0}{lim}f\left(x\right)\right)$

Beispiel 5 - 1: