How to evaluate $lim_{xto 0} frac {(sin(2x)-2sin(x))^4}{(3+cos(2x)-4cos(x))^3}$?
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$$lim_{xto 0} frac {(sin(2x)-2sin(x))^4}{(3+cos(2x)-4cos(x))^3}$$ 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
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edited Jan 8 at 18:17
Andrei
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asked Jan 8 at 18:14
iggykimi iggykimi
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