若limx→∞[(2x2+1)/(x-1)-ax-b]=0,求a,b的值.
limx→∞[(2x2+1)/(x-1)-ax-b] =limx→∞{[2x2+1-ax(x-1)-b(x-1)]/(x-1)} =limx→∞{[(2-a)x2+(a-b)x+b+1]/(x-1)}=0 故分子必须是零次多项式,即 {2-a=0, a-b=0, 所以 {a=2, b=2.
若limx→∞[(2x2+1)/(x-1)-ax-b]=0,求a,b的值.
limx→∞[(2x2+1)/(x-1)-ax-b] =limx→∞{[2x2+1-ax(x-1)-b(x-1)]/(x-1)} =limx→∞{[(2-a)x2+(a-b)x+b+1]/(x-1)}=0 故分子必须是零次多项式,即 {2-a=0, a-b=0, 所以 {a=2, b=2.