Question

Lim((5*x-1)/(5*x))^(4*x)

Answer 1

$lim_{x to infty} ( frac{5x-1}{5x} )^{4x}=> lim_{x to infty} (1+ frac{1}{5x-1})^{-4x};$
$lim_{x to infty}((1+ frac{1}{5x-1})^{5x-1})^{ lim_{xto infty} ( frac{-4x}{5x-1})}$
Используем второй замечательный предел:
$e^{ lim_{x to infty} ( frac{-4x}{5x-1})}=e^{ -frac{4}{5}$