[tex]sin(2x)=2sin(x)cos(x)\\[/tex]
[tex]\lim_{n \to 0} \frac{sin(x)}{x} = 1[/tex] - первый замечательный предел
[tex]\lim_{n \to 0} \frac{sin^2(2x)cos(x)}{x^2} = (\frac{0}{0}) = \lim_{n \to 0} \frac{(2sin(x)cos(x))^2cos(x)}{x^2} = \\ = 4\lim_{n \to 0} \frac{sin^2(x)}{x^2}\lim_{n \to 0} cos^3(x) = 4(\lim_{n \to 0} \frac{sin(x)}{x})^2\lim_{n \to 0} cos^3(x) = \\ = 4*1*cos^3(0)= 4[/tex]