Question

求极限X趋于O x^2sinx分之tanx-x 麻烦说一下过程，谢谢

Answer 1

lim(x->0) (tanx-x)/(x^2sinx)
=lim(x->0) (tanx-x)/x^3 (0/0)
=lim(x->0) ((secx)^2-1)/(3x^2) (0/0)
=lim(x->0) 2(secx)^2.tanx/(6x)
= (1/3)lim(x->0) (secx)^2
= 1/3

追问

lim(x->0) (tanx-x)/(x^2sinx) 变成 lim(x->0) (tanx-x)/x^3 是不是分子分母同时乘了一个X吗
lim(x->0) 2(secx)^2.tanx/(6x)变成 (1/3)lim(x->0) (secx)^2是怎么变得，麻烦说一下好吗，谢谢

追答

sinx ~ x (x->0)
tanx ~x (x->0)