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  \Large{7. Gyak. \\
  Teljes fv. vizsgálat, L'Hospital szabály}
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\bigskip

\begin{enumerate}

 \item  Végezzen teljes függvény vizsgálatot!
  \begin{enumerate} 
    \item $f(x)=\frac{x^3-2x^2+x}{x^2-1}$
    \item $f(x)=\frac{x^3}{x^2-3}$
	\item $f(x)=\sqrt[3]{x} (1-x)^{\frac23}$
	\item $f(x)=\frac{e^x}{1+e^x}$
	\item $f(x)=\ln \left| x-\sqrt{x^2-1} \right|$
  \end{enumerate}
  
 \item 
  \begin{enumerate}
   \item $\lim_{x\to 0}= \frac{\ln(1-x)+x^2}{(1+x)^5+x^2-1}?$
   \item $\lim_{x\to 0}= \frac{e^{-x^2}-1+x^2}{x^4}?$
   \item $\lim_{x\to +\infty} \frac{\ln\left( 2+3 e^x \right)}{\sqrt{3+2x}}=?$
   \item $\lim_{x\to \infty} \left( \ln \left( 1+\frac{1}{x}\right) -\frac{1}{x+1}\right)=?$
   \item $\lim_{x\to 0} \left( \sqrt{\cos 2x} - \sqrt{\cos 3x}\right)\cdot \frac{1}{x^2}=?$
   \item $\lim_{x\to 0_+} \left(\frac{1}{x}\right)^x =?$
  \end{enumerate}
 
 \end{enumerate}
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