JEE Main 2021 (Online) 27th August Evening ShiftQuestion 1
If $\lim_{x\to\infty}\left(\sqrt{x^{2}-x+1}-ax\right)=b$, then the ordered pair $(a,b)$ is :
Limits & Continuity
Solution
For finite limit need $a=1$ (else the expression $\to\pm\infty$). $\sqrt{x^2-x+1}-x=\frac{-x+1}{\sqrt{x^2-x+1}+x}\to\frac{-1}{2}$. So $(a,b)=(1,-\tfrac12)$. Option (B).