How to evaluate $lim_{xto 0} frac {(sin(2x)-2sin(x))^4}{(3+cos(2x)-4cos(x))^3}$?
1
$begingroup$
$$lim_{xto 0} frac {(sin(2x)-2sin(x))^4}{(3+cos(2x)-4cos(x))^3}$$ without L'Hôpital. I've tried using equivalences with ${(sin(2x)-2sin(x))^4}$ and arrived at $-x^{12}$ but I don't know how to handle ${(3+cos(2x)-4cos(x))^3}$ . Using $cos(2x)=cos^2(x)-sin^2(x)$ hasn't helped, so any hint?
real-analysis limits-without-lhopital
share | cite | improve this question
edited Jan 8 at 18:17
Andrei
11.6k 2 10 26
asked Jan 8 at 18:14
iggykimi iggykimi