Question

已知

lim

x→2

x2+cx+2

x-2

=a，則a²-c²的值為

-8

．

Answer 1

分析：由

lim

x→2

x2+cx+2

x-2

=a，知4+2c+2=0，解得c=-3．故a=

lim

x→2

x 2-3x+2

x-2

=

lim

x→2

(x-2)(x-1)

x-2

=1，由此能求出答案．

解答：解：∵

lim

x→2

x2+cx+2

x-2

=a，
∴4+2c+2=0，
解得c=-3．
∴

lim

x→2

x2+cx+2

x-2

=a
=

lim

x→2

x 2-3x+2

x-2

=

lim

x→2

(x-2)(x-1)

x-2

=

lim

x→2

（x-1）
=1．
∴a²-c²=1-9=-8．
故答案為：-8．

點(diǎn)評：本題考查極限的運(yùn)算，解題時(shí)要認(rèn)真審題，仔細(xì)解答，注意極限逆運(yùn)算的靈活運(yùn)用．