Question

求极限问题 如图

后面计算步骤，是怎么=1/16的啊

Answer 1

x->0
tanx = x +(1/3)x^3 +o(x^3)
sinx = x -(1/6)x^3 +o(x^3)
tanx - sinx = (1/2)x^3 +o(x^3)
lim(x->0) (tanx - sinx)/(sin2x)^3
=lim(x->0) (1/2)x^3/(2x)^3
= 1/16

追问

我想问的是1/16是怎么算出来的啊，

追答

(sin2x)^3 =(2x)^3 +o(x^3)
tanx - sinx = (1/2)x^3 +o(x^3)
lim(x->0) (tanx - sinx)/(sin2x)^3
等价交换
=lim(x->0) (1/2)x^3/(2x)^3
=lim(x->0) (1/2)x^3/(8x^3)
= (1/2) /8
= 1/16