Question

tanx-x/x-arcsinx求极限

Answer 1

x->0
tanx =x+(1/3)x^3+o(x^3)
tanx -x=(1/3)x^3+o(x^3)
arcsinx = x+(1/6)x^3+o(x^3)
x-arcsinx = -(1/6)x^3+o(x^3)
lim(x->0) (tanx-x)/(x-arcsinx)
=lim(x->0) (1/3)x^3/[-(1/6)x^3]
=-2