Q120 / 180 · COMEDK 2014 · Mathematics

$\lim _{x \rightarrow-\infty} \frac{2 x-1}{\sqrt{x^{2}+2 x+1}}$ is equal to

  • A
    2
  • Correct answer
    B
    $-2$
  • C
    1
  • D
    $-1$

Solution

$\lim _{x \rightarrow-\infty} \frac{2 x-1}{\sqrt{x^{2}+2 x+1}}$ $=\lim _{y \rightarrow \infty} \frac{-2-\frac{1}{y}}{\sqrt{1-\frac{2}{y}+\frac{1}{y^{2}}}} \quad[$ put $x=-y, x \rightarrow-\infty]$ $=-\frac{2}{1}=-2$

Hence, the correct answer is option: 'B'.

Relevant Questions