能
lim[(x^2+3x+4)/(x+1)-ax+b]
=lim{(x^2+3x+4)/(x+1)-[ax^2+(a+b)x+b]/(x+1)}
=lim[(1-a)x^2+(3-a-b)x+4-b]/(x+1)
要使上式有极限,须(1-a)x^2+(3-a-b)x+4-b与x+1是同阶无穷大,
故1-a=0,有a=1
lim[(1-a)x^2+(3-a-b)x+4-b]/(x+1)
=lim[(2-b)x+4-b]/(x+1)
=lim(2-b)=2
b=0