Question

lim x->0 1-cos4x/x*2

Answer 1

$lim_{x to 0} frac{1-cos4x}{ x^{2} } = lim_{x to 0} frac{1-(1-2 sin^{2} 2x)} {x^{2} } = lim_{x to 0} frac{2sin ^{2}2x }{ x^{2} } =$
$=2* lim_{x to 0} ( frac{sin2x}{x} ) ^{2} =2* lim_{x to0} ( frac{2sinx*cosx}{x} ) ^{2} =$
$=2* lim_{x to0} (4 cos^{2}x*( frac{sinx}{x} ) ^{2} )=8* lim_{x to0} cos^{2} x* lim_{x to0} ( frac{sinx}{x} )^{2} =$
$=8*1* ( lim_{x to 0} frac{sinx}{x} )^{2} =8* 1^{2} =8$

Answer 2

Спасибо!