解：lim [(x³+1)/(x²+1) -ax-b]x→∞=lim [(x³+x-x+1)/(x²+1) -ax-b]x→∞=lim [x - (x-1)/(x²+1) -ax-b]x→∞=lim [(1-a)x -(x-1)/(x²+1) -b]x→∞=01-a=0，b=0解得a=1，b=0
