lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.

lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.
lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.

lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.
lim(x→-2)(ax+b)/(x+2)=lim(x→-2)[a(x+2)+b-2a]/(x+2)=a+lim(x→-2)(b-2a)/(x+2)
由于lim(x→-2)1/(x+2)=∞
所以lim(x→-2)(b-2a)/(x+2)为常数的条件是b-2a=0,即b=2a
那么lim(x→-2)(ax+b)/(x+2)=a=4,故b=8

分子在x=-2时为零，故-2a+b=0，且左边的极限为a/1=4，故b=8,a=4

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