Определите предел функции:

По формуле
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$\lim_{x \to 0} tg2x\cdot(ln(ctgx))= \lim_{x \to 0} \frac{ln(ctgx)}{ctg2x}=( \frac{\infty}{\infty})= \\ = \lim_{x \to 0} \frac{(ln(ctgx))`}{(ctg2x)`}= \lim_{x \to 0} \frac{ \frac{1}{ctgx}(ctgx)` }{ \frac{1}{sin ^{2}2x }\cdot 2 }= \lim_{x \to 0} \frac{sin ^{2}2x }{2ctgx\cdot sin ^{2}x }= \\ = \lim_{x \to 0} \frac{4sin ^{2}x\cdot cos ^{2}x }{2sinx\cdot cosx} =0$