Question

求limsinx-xcosx/x^3在x趋向于0的极限

Answer 1

泰勒展开：

sinx=x+x^3/6+o(x^4)

cosx=1+x^2/2+o(x^3)

limsinx-xcosx/x^3

=lim(x+x^3/6-x(1+x^2/2)+o(x^3))/x^3

=lim(-x^3/3+o(x^3))/x^3

=-1/3