Question

lim(x趋于无穷)[x^2/(x+1)-ax-b)=0,求a和b的值

Answer 1

x^2/(x+1)-ax-b
=x-1 + 1/(x+1) -ax-b
=x(1-a) +(-1-b) +1/(x+1)
要使x趋于无穷时
lim(x趋于无穷)[x^2/(x+1)-ax-b)=0
则1-a=0
-1-b=0
所以，a=1,b=-1

Answer 2

[x^2/(x+1)-ax-b)]=[(1-a)x^2-(a+b)x-b]/(1+x)=[(1-a)x-(a+b)-b/x](1+1/x)],
lim(x趋于无穷)[(1-a)x-(a+b)-b/x](1+1/x)]=0,则1-a=0, a+b=0, 所以a=1,b=-1