求lim(x^3(sin1/x-1/2*sin2/x)) x趋于无穷

问题描述:

求lim(x^3(sin1/x-1/2*sin2/x)) x趋于无穷

lim(x^3(sin1/x-1/2*sin2/x)) x趋于无穷
=lim(sint-1/2*sin2t)/t^3 t趋于0
=lim(cost-cos2t)/3t^2 t趋于0
=lim(-sint+2sin2t)/6t t趋于0
=lim(-cost+4cos2t)/6 t趋于0
=(-1+4)/6
=1/2