IIT-JEE 2012 · Paper 1 · Mathematics Q44

MathematicsSingle correct+3 / -1Question 44 of 60

If $\displaystyle\lim_{x\to\infty}\left(\frac{x^2+x+1}{x+1}-ax-b\right)=4$ , then

a=1,\ b=4

a=1,\ b=-4

a=2,\ b=-3

a=2,\ b=3

Answer and worked solution

Official answer: B

Divide. $\dfrac{x^2+x+1}{x+1}=x+\dfrac1{x+1}$ . So the expression is
$(1-a)x-b+\frac1{x+1}.$

Finite limit 4. The $x$ term must vanish, $a=1$ , and then $-b=4$ , so $b=-4$ .

(B)

Topics:Limits

IIT-JEE 2012 · Paper 1, Mathematics question 44