<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">Dokažte, že funkce $f(x) = |x|^{\alpha}\cos{1 \over x}$ pro
$x \not = 0$ a $f(0) = 0$
nemá (resp. má) pro $\alpha \in (0,1]$
(resp. $\alpha \in (1, +\infty)$) na intervalu $[-1,1]$ konečnou
 variaci.
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