{Najdi limitu
$$
   \lim_{x\to2}\frac{{(x^2-x-2)}^{20}}{{(x^3-12x+16)}^{10}}.
$$}{
\begin{eqnarray*}
   \lim_{x\to2}\frac{{(x^2-x-2)}^{20}}{{(x^3-12x+16)}^{10}} & = &
      \lim_{x\to2}\frac{{(x+1)}^{20}
                        {(x-2)}^{20}}
                       {{{(x-2)}^{10}}^2
                        {(x+4)}^{10}}\\
   & = & \lim_{x\to2}\frac{{(x+1)}^{20}} {{(x+4)}^{10}}\\
   & = & \frac{3^{20}}{6^{10}}\;=\;\frac{3^{20}}{3^{10}\cdot2^{10}}\;=
         \;{\left(\frac32\right)}^{10}.
\end{eqnarray*}
}
