If `lim_(xtooo) {(x^3+1)/(x^2+1)-(ax+b)}=2`, then

Options

A. a = 1 and b = 1
B. a = 1 and b = -1
C. a = 1 and b = -2
D. a = 1 and b = 2

Answer

C

Explanation

Given that,
`lim_(xtooo)[(x^(3)+1)/(x^(2)+1)-(ax-b)]=2`
`rArr lim_(xtooo) [(x^(3) (1-a)-bx^(2)-ax +(1-b))/(x^(2)+1)]=2`
`rArr lim_(xtooo)[(x(1-a)-b-(a)/(x)+((1-b))/(x^(2)))/(1+(1)/(x^(2)))]=2`
This, limit will exist, if
1 -a = 0 and b = -2
`rArr a = 1 and b = -2`