Question

若

lim

x→-∞

(

x2-x+1

+x-k)=1，則k=

 

．

Answer 1

考點：極限及其運算

專題：導數的綜合應用

分析：變形

x2-x+1

+x-k=

(2k-1)x+1-k2

x2-x+1 -(x-k)

=

(2k-1)+ 1-k2 x

- 1+ 1-x x2 -1+ k x

，再利用極限的運算性質即可得出．

解答： 解：∵

x2-x+1

+x-k=

(2k-1)x+1-k2

x2-x+1 -(x-k)

=

(2k-1)+ 1-k2 x

- 1+ 1-x x2 -1+ k x

，
∴

lim

x→-∞

(

x2-x+1

+x-k)=

2k-1

-2

=1，解得k=-

1

2

．
故答案為：-

1

2

．

點評：本題考查了極限的運算性質、變形能力，屬于基礎題．