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Vypo�t�te:

$$\lim\limits_{x \to 0} {x + \log{(1+x)} \over 2x - \log{(1+x)}}$$

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Proto�e limita $\lim\limits_{x \to 0} {\log{(1+x)} \over x}$ je rovna ��slu 1, plat�:

$$\lim\limits_{x \to 0} {x + \log{(1+x)} \over 2x - \log{(1+x)}} = \lim\limits_{x \to 0} {1 + {\log{(1+x)} \over x} \over 2 - {\log{(1+x)} \over x}} = 2$$



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