<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">Spočtěte pomocí Taylorova vzorce:
$$
    \lnul\frac{a^x + a^{-x} - 2}{x^2}.
$$
\reseni
\begin{multline*}
    \lnul\frac{a^x + a^{-x} - 2}{x^2} =
    \lnul\frac{e^{x\log a} + e^{-x\log a} - 2}{x^2} =\\
    \lnul\frac{1 + x\log a + \frac{(x\log a)^2}2 + 1 - x\log a + \frac{(x\log a)^2}2 - 2}{x^2} =\\
   =\lnul\frac{(x\log a)^2}{x^2} = \lnul\frac{x^2\log^2a}{x^2} = \log^2a.
\end{multline*}
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