Änderungen

6 Bytes hinzugefügt ,  18:03, 29. Jan. 2013
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\begin{eqnarray}
 
\begin{eqnarray}
2f'(x_{0})f(x_{0})=2 \lim\limits_{x \rightarrow x_{0}}{\frac{f(x)-f(x_{0})}{x-x_{0}}f(x_{0})}= \lim\limits_{x \rightarrow x_{0}}{\frac{f(x)-f(x_{0})}{x-x_{0}}(f(x_{0})+f(x_{0}))}\\
+
2f'(x_{0})f(x_{0})&=&2 \lim\limits_{x \rightarrow x_{0}}{\frac{f(x)-f(x_{0})}{x-x_{0}}f(x_{0})}\\
 +
&=&\lim\limits_{x \rightarrow x_{0}}{\frac{f(x)-f(x_{0})}{x-x_{0}}(f(x_{0})+f(x_{0}))}\\
 
&=&\lim\limits_{x \rightarrow x_{0}}{\frac{f(x)-f(x_{0})}{x-x_{0}}\lim\limits_{x \rightarrow x_{0}}(f(x)+f(x_{0}))}\\
 
&=&\lim\limits_{x \rightarrow x_{0}}{\frac{f(x)-f(x_{0})}{x-x_{0}}\lim\limits_{x \rightarrow x_{0}}(f(x)+f(x_{0}))}\\
 
&=&\lim\limits_{x \rightarrow x_{0}}{\frac{(ff)(x)-(ff)(x_{0})}{x-x_{0}}}\\
 
&=&\lim\limits_{x \rightarrow x_{0}}{\frac{(ff)(x)-(ff)(x_{0})}{x-x_{0}}}\\