请问这道数学题怎么做，详细步骤，谢谢

答案应该选C。用排除法来做，将选项的临界值代入函数中，F（-1）=SIN（-3）/8，可知sin-3小于零，那么f（-1）小于零。此函数F（0）=0，以此类推，可选出c，函数在（1，2）可以

ans: A (-1,0)

f(x)= |x|sin(x-2)/[x(x-1)(x-2)^2]

lim(x->0-) f(x)

=lim(x->0-)  -xsin(x-2)/[x(x-1)(x-2)^2]

=-(1/4)sin2

lim(x->0+) f(x)

=lim(x->0+)  xsin(x-2)/[x(x-1)(x-2)^2]

=lim(x->0+)  sin(x-2)/[(x-1)(x-2)^2]

=sin(-2)/(0-1)(0-2)^2

=(1/4)sin2

lim(x->1-) f(x)

=lim(x->1-)  xsin(x-2)/[x(x-1)(x-2)^2]

=lim(x->1-)  sin(x-2)/[(x-1)(x-2)^2]

->+无穷

lim(x->2-) f(x)

=lim(x->2-)  xsin(x-2)/[x(x-1)(x-2)^2]

=lim(x->2-)  sin(x-2)/[(x-1)(x-2)^2]

->-无穷

lim(x->2+) f(x)

=lim(x->2+)  xsin(x-2)/[x(x-1)(x-2)^2]

=lim(x->2+)  sin(x-2)/[(x-1)(x-2)^2]

->+无穷

证明：在△ABC中，AB=AC
∴∠B=∠C
∵D是BC中点，所以BD=CD
∴△ABD≌△ACD
∴S△ABD=S△ACD
∵DE⊥AB,DF⊥AC
∴AB*DE=AC*DF
∵AB=AC
∴DE=DF