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Vypo�t�te limitu:

$$\lim\limits_{x \to 0} \left(\cot x - {1 \over x}\right)$$

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Jde o limitu typu $\infty - \infty$. Funkci $\cot$ nahrad�me pod�lem ${\cos x \over \sin x}$ a v�raz v z�vork�ch p�evedeme na spole�n�ho jmenovatele. M�me tedy:

$$\lim\limits_{x \to 0} \left(\cot x - {1 \over x}\right) = \lim\limits_{x \to 0} {x\cos x - \sin x \over x \sin x} = \lim\limits_{x \to 0} {\cos x - x \sin x - \cos x \over \sin x + x \cos x} =$$

$$= \lim\limits_{x \to 0} {-x\sin x \over \sin x + x \sin x} = \lim\limits_{x \to 0} { - \sin x - x \cos x \over \cos x + \cos x - x \sin x} = 0$$





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