Question

若lim(x趋于无穷)((x^2+3x+4)/(x+1)-ax+b)=2,则a,b的值分别是?

Answer 1

lim(x→∞)(x^2+3x+4)/(x+1)-ax+b)

=lim(x→∞)[(x+1)^2+x+1+2)/(x+1)-ax+b

=lim(x→∞)(x+1)+1+2/(x+1)-ax+b

=lim(x→∞)(1-a)x+2+b+2/(x+1)

=2

1-a=0,a=1

2+b=2,b=0