Question

Lim x-> 0 cos 2x - sin 2x / 4x

Answer 1

$lim_{x to inft0} (cos 2x - sin 2x / 4x)=lim_{x to inft0} cos 2x - lim_{x to inft0} frac{sin 2x}{4x} = \ \ =1- frac{1}{2} lim_{x to inft0} frac{sin 2x}{2x}=1-frac{1}{2}=frac{1}{2}$