Spoètìte pomocí Taylorova vzorce:
$$
    \linf\left(\sqrt[6]{x^6+x^5} - \sqrt[6]{x^6-x^5}\right).
$$
\reseni
\begin{multline*}
    \linf\left(\sqrt[6]{x^6+x^5} - \sqrt[6]{x^6-x^5}\right) =
    \linf x\left(\sqrt[6]{1+\frac1x} - \sqrt[6]{1-\frac1x}\right) =\\
   =\lnpl \frac{\sqrt[6]{1+x} - \sqrt[6]{1-x}}x =
    \lnpl \frac{(1+x)^{1/6} - \bigl(1+(-x)\bigr)^{1/6}}x =\\
   =\lnpl \frac{1+\frac x6 + o(x) - 1+\frac x6 - o(x)}x =
    \lnpl \frac{x + o(x)}{3x} = \frac13.
\end{multline*}
