若limx→无穷大[(x2+1)/(x+1)-(ax+b)]=0,求a,b
问题描述：
若limx→无穷大[(x2+1)/(x+1)-(ax+b)]=0,求a,b
答
x→∞时[(x^2+1)/(x+1)-(ax+b)]
→[x^2+1-(x+1)(ax+b)]/(x+1)
→[(1-a)x^2-(a+b)x+1-b]/(x+1)
→0,
∴1-a=0,a+b=0,
∴a=1,b=-1.