Question

If lim
x→∞[x2+1x+1−ax−b]=∞Ltx→∞[x2+1x+1−ax−b]=∞.

• A. $b$ can have any value.
• B. $a$ can have any value
• C. $b$ can have any value. except 1
• D. $a$ can have any value. except 1

Answer 1

Answer: (A), (D)

$a$ can have any value. except 1
$b$ can have any value.

$\underset{x\to \infty }{lim}\frac{x^2(1-a)-x(a+b)+(1-b)}{x+1}=\infty$
Above will be possible if degree of $N^r$ is greater than degree of $D^r$
$\therefore 1-a\ne 0i.e.,a\ne 1$ and b can have any value.
Ans: A,D