If `lim_(xtooo)((x^(2)+1)/(x+1)-ax-b)=0`, find the values of a and b.

Options

A. `a=1,b=1`
B. `a=-1,b=1`
C. `a=1,b=-1`
D. `a=-1,b=-1`

Answer

C

Explanation

We have ,
`lim_(n to oo) {(x^2+1)/(x+1)-ax-b}=0`
`rArr lim_(x to oo) (x^2(1-a)-x(a+b)+1-b)/(x+1)=0`
Since the limit of the given expression is zero. Therefore, degree of the polynomial in numerator must be less than that of denominator. As the denominator is a first degree polynomial. So, numerator must be a constant i.e., a zero degree polynomial.
`therefore 1-a =0 and a +b =0 rArr a=1 and b = 1`.