Question

求极限limx→o (cossinx-cosx)/(x2(1-cosx))=?

Answer 1

常用等价无穷小x→0时,1-cosx~x²/2,sinx→0时,cossinx~1-sin²x/2,则limx→o (cossinx-cosx)/(x²(1-cosx))=limx→o(1-sin²x/2-cosx)/(x²(1-cosx))=limx→o(1-cosx)²/(2x²(1-cosx))=limx→o(1-cosx)/2x²=(x²/2)/2x²=1/4.