Question

Найти предел желательно по действиям

Answer 1

$\begin{array}{l} \lim \limits_{x\to 0}\left( 1-5x\right) ^{tg2\left( x-\frac{\pi }{4} \right) }\\ \lim \limits_{x\to 0}\left( \left( 1+\left( -5x\right) \right) ^{-\frac{1}{5x} }\right) ^{\left( -5x\right) tg2\left( x-\frac{\pi }{4} \right) }\\ e^{\lim \limits_{x\to 0}\left( \frac{-5x}{ctg(2x-\frac{\pi }{4} )} \right) }\\ e^{\lim \limits_{x\to 0}\left( \frac{5x}{ctg(\frac{\pi }{4} -2x)} \right) }=e^{\lim \limits_{x\to 0}(\frac{5x}{tg2x} )}\\ e^{\lim \limits_{x\to 0}\left( \frac{5}{\frac{2}{cos^{2}2x} } \right) }=e^{\frac{5}{\frac{2}{cos^{2}0} } }=e^{\frac{5}{2} }. \end{array}$