Question

求极限 lim(x→0) (x-tanx)/x²(2x-tanx)

Answer 1

x->0
tanx= x+(1/3)x^3+o(x^3)
x-tanx=-(1/3)x^3+o(x^3)
lim(x->0) (x-tanx)/[x^2.(2x-tanx)]
=lim(x->0) (x-tanx)/x^3
=lim(x->0) -(1/3)x^3/x^3
=-1/3