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Vypo�teme limitu 

$$\lim\limits_{x \to 1} \left[ (1-x) \tan {\pi x \over 2} \right].$$


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Jde o limitu typu $0 . \infty$ Nejprve dan� v�raz uprav�me na v�raz typu $0 / 0$ a pak pou�ijeme l'Hospitalova pravidla:

$$\lim\limits_{x \to 1} \left[ (1-x) \tan {\pi x \over 2} \right] = \lim\limits_{x \to 1} {1-x \over \cot {\pi x \over 2}} = \lim\limits_{x \to 1} {-1 \over {-1 \over \sin^2 {\pi x \over 2}} {\pi \over 2}} = {2 \over \pi}$$


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