Q. $\lim_{x \rightarrow \infty}{\lbrack\sqrt{x^{2} + 2x - 1} - x\rbrack}$ is equal to
A) $\infty$
B) $\frac{1}{2}$
C) 4
D) 1
Explanation
(d)
$\lim_{x \rightarrow \infty}{\lbrack\sqrt{x^{2} + 2x - 1} - x\rbrack} = \lim_{x \rightarrow \infty}{\lbrack\frac{x^{2} + 2x - 1 - x^{2}}{\sqrt{x^{2} + 2x - 1} + x}\rbrack}$
$= \lim_{x \rightarrow \infty}\left\lbrack \frac{2 - \frac{1}{x}}{\sqrt{1 + \frac{2}{x} - \frac{1}{x^{2}}} + 1} \right\rbrack = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.