仅供参考
(1)
f(x)
=xlnx/(1-x) ; x>0, x≠1
=R ; x=1
y=1-x
lim(x->1) f(x)
=lim(x->1) xlnx/(1-x)
=lim(y->0) (1-y)ln(1-y)/y
=lim(y->0) -(1-y)
=-1
=>
R=-1
(2)
f(x)
=sinx/(x-x^2) ; x≠0
=0 ; x=0
lim(x->0) f(x)
=lim(x->0) sinx/(x-x^2)
=lim(x->0) 1/(1-x)
=1
≠f(0)
x=0 : 间断点
/
x=1
lim(x->1) f(x)
=lim(x->1) sinx/(x-x^2)
不存在
x=1 : 间断点
(3)
x^5-5x-1=0
f(1) = 1-5-1 = -5<0
f(2) =32-10-1 =21>0
在（1,2) x^5-5x-1=0 至少有一个根
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