Question

lim

x→0

(

1

x2-x

-

2

x2-2x

)=

 

．

Answer 1

分析：先通分，然后消除零因子，把

lim

x→0

(

1

x2-x

-

2

x2-2x

)化简为

lim

x→0

-1

(x-1)(x-2)

，由此能够导出其结果．

解答：解：

lim

x→0

(

1

x2-x

-

2

x2-2x

)=

lim

x→0

[

1

x(x-1)

-

2

x(x-2)

]
=

lim

x→0

x-2-2x+2

x(x-1)(x-2)

=

lim

x→0

-1

(x-1)(x-2)

=-

1

2

．
故答案为：-

1

2

．

点评：本题考查极限的运算，解题时要认真审题，仔细求解，注意消除零因子．