displaystyle limx → -∞(2x-1/√x2+2x+1)=

Question

displaystyle limx → -∞(2x-1/√x2+2x+1)= (A) 2 (B) -2 (C) 1 (D) -1

Tardigrade Admin · Accepted Answer

displaystyle limx → -∞(2x-1/√x2+2x+1) Put x =-1/y as x → -∞, y → 0 = displaystyle limy → 0(-(2/y)-1/√(1)y2-(2)y+1 = displaystyle lim/y → 0)(-2-y/√1-2y+y2) =-2.

Q. $x \to - \infty lim$ $\frac{2 x - 1}{x ^{2} + 2 x + 1} =$

$2$

$- 2$

$1$

$- 1$

$x \to - \infty lim$ $\frac{2 x - 1}{x ^{2} + 2 x + 1}$
Put $x = - 1/ y$ as $x \to - \infty$ , $y \to 0$
$= y \to 0 lim$ $\frac{- \frac{2}{y} - 1}{\frac{1}{y ^{2}} - \frac{2}{y} + 1}$
$= y \to 0 lim$ $\frac{- 2 - y}{1 - 2 y + y ^{2}}$
$= - 2$ .

Q. x→−∞lim​x2+2x+1​2x−1​=

2

−2

1

−1

x→−∞lim​x2+2x+1​2x−1​ Put x=−1/y as x→−∞, y→0 =y→0lim​y21​−y2​+1​−y2​−1​ =y→0lim​1−2y+y2​−2−y​ =−2.

Q. $x \to - \infty lim$ $\frac{2 x - 1}{x ^{2} + 2 x + 1} =$

$2$

$- 2$

$1$

$- 1$

$x \to - \infty lim$ $\frac{2 x - 1}{x ^{2} + 2 x + 1}$
Put $x = - 1/ y$ as $x \to - \infty$ , $y \to 0$
$= y \to 0 lim$ $\frac{- \frac{2}{y} - 1}{\frac{1}{y ^{2}} - \frac{2}{y} + 1}$
$= y \to 0 lim$ $\frac{- 2 - y}{1 - 2 y + y ^{2}}$
$= - 2$ .