Запишиответ

Вычислипредел \(\lim\limits\_{x\rarr0}\cfrac{\sin5x}{\tg4x}\) .

Решение.

\(\lim\limits\_{x\rarr0}\cfrac{\sin5x}{\tg4x}=\lim\limits\_{x\rarr0}\cfrac{\sin5x\cdot4x\cdot\cos4x\cdot5}{5x\cdot\sin4x\cdot4}\=\lim\limits\_{x\rarr0}\left(\cfrac{\sin5x}{5x}\cdot\cfrac{4x}{\sin4x}\cdot\cos4x\cdot\cfrac{5}{4}\right)=\cfrac{5}{4}\cdot\lim\limits\_{x\rarr0}\cfrac{\sin5x}{5x}\cdot\cfrac{1}{\lim\limits\_{x\rarr0}\cfrac{\sin4x}{4x}}\cdot\lim\limits\_{x\rarr0}\cos4x=\) [ ].