Question

求极限值是多少

Answer 1

如图所示

追问

你的代换错了这种情况下tanx不能代换成x

Answer 2

-2/3到无穷大，

Answer 3

lim(x->0) [ 1/x^2 -1/(tanx)^2 ]
=lim(x->0) [(tanx)^2 -x^2 ]/[x^2 .(tanx)^2]
=lim(x->0) [(tanx)^2 -x^2 ]/x^4 (0/0 分子分母分别求导)
=lim(x->0) [2(tanx).(secx)^2 -2x ]/(4x^3)
=lim(x->0) [2sinx -2x.(cosx)^3 ]/[4x^3. (cosx)^3 ]
=lim(x->0) [sinx -x.(cosx)^3 ]/(2x^3 ) (0/0 分子分母分别求导)
=lim(x->0) [cosx +3x.(cosx)^2.sinx - (cosx)^3 ]/(6x^2)
=lim(x->0) [1 +3x.cosx.sinx - (cosx)^2 ]/(6x^2)
=lim(x->0) [(sinx)^2 +3x.cosx.sinx ]/(6x^2)
=lim(x->0) [ (sinx)^2 +(3/2)xsin(2x) ]/(6x^2)
=lim(x->0) [ x^2 +(3/2)(x)(2x) ]/(6x^2)
=lim(x->0) 4x^2 /(6x^2)
=2/3