Pro mal� $|x|$ odvodit jednoduchou p�ibli�nou formuli pro v�raz:
$$
    \frac{\log 2}{\log\left(1 + \frac{x}{101}\right)}.
$$
\reseni K odvozen� formule pou�ijeme Taylor�v vzorec:
$$
    \frac{\log 2}{\log\left(1 + \frac{x}{101}\right)} = \frac{\log 2}{\frac{x}{101} + o(x)},\; x\to0.
$$
V�raz $o(x)$ je mal� pro mal� $x$, proto jej m��eme zanedbat, ��m� dostaneme po�adovanou formuli:
$$
    \frac{\log 2}{\frac{x}{101} + o(x)}=\frac{\log 2}{\frac x{101}}=\frac{101\cdot \log 2}{x}
    \approx\frac{70}{x}.
$$
