Question

Given that `lim_(x->oo)((x^2)/(1+x)-ax-b)`, find the values of `a` and `b` ?

Answer 1

See below.

Explanation:

We have

`x^2 = (x+1)(x-1)+1` then

`lim_(x->oo)(x^2/(x+1)-ax-b) = lim_(x->oo)((x-1)+1/(x+1)-ax-b) =`

`=lim_(x->oo)(x-1-ax-b)` Now choosing `a=1` we get

`lim_(x->oo)(x^2/(x+1)-(1)x-b)=-(b+1)`