_ x - 2 x-1 x^2+2 x+1 is equal to - Vidyadip

MCQ

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

A
2
✓
-2
C
1
D
-1

✓

Answer

Correct option: B.

-2

(B)
Put $x=-y$
As $x \rightarrow-\infty, y \rightarrow \infty$
$\therefore \quad \lim _{x \rightarrow-\infty} \frac{2 x-1}{\sqrt{x^2+2 x+1}}=\lim _{y \rightarrow \infty} \frac{-2 y-1}{\sqrt{(-y)^2-2 y+1}}$
$=\lim _{y \rightarrow \infty} \frac{-2-\frac{1}{y}}{\sqrt{1-\frac{2}{y}+\frac{1}{y^2}}}=-\frac{2}{1}=-2$

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