The correct option is B −2
limx → 0sin(x2)ln(cos(2x2−x))
limx → 0sin(x2)log(1−2sin2(2x2−x2))
limx → 0sin(x2)x2x2 log(1−2sin2(2x2−x2))−2 sin2(2x2−x2)[−2 sin2(2x2−x2)]
=limx → 0−x22sin2(2x2−x2)(2x2−x2)21(2x2−x2)2
=limx → 0−2x2(2x2−x)2=limx → 0−2(2x−1)2=−2