请问这道数学题怎么做,详细步骤,谢谢 20
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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
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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
∴∠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
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