Spoètìte pomocí Taylorova vzorce:
$$
    \linf x^{\frac32}\left(\sqrt{x+1} + \sqrt{x-1} - 2\sqrt x\right).
$$
\reseni
\begin{multline*}
    \linf x^{\frac32}\left(\sqrt{x+1} + \sqrt{x-1} - 2\sqrt x\right) =\\
   =\linf x^{\frac32}\sqrt x\left(\sqrt{1+\frac1x} + \sqrt{1-\frac1x} - 2\right)=\\
   =\lnpl \frac{\sqrt{1+x} + \sqrt{1-x} - 2}{x^2} =\\
   =\lnpl\frac{1 + \frac x2 - \frac{x^2}8 + o(x^2) + 1 - \frac x2 - \frac{x^2}8 + o(x^2) -2}{x^2}=-\frac14.
\end{multline*}
