The value of displaystyle lim x arrow ∞(√x+√x+√x-√x) is

Question

The value of displaystyle lim x arrow ∞(√x+√x+√x-√x) is (A) (1/2) (B) 1 (C) 0 (D) None of these

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow ∞[√x+√x+√x-√x] = displaystyle lim x arrow ∞ (x+√x+√x-x/√x+√x+√x+√x) = displaystyle lim x arrow ∞ (√x+√x/√x+√x+√x+√x) = displaystyle lim x arrow ∞ (√x/√x[(1+(1)√x √1+(1)√x)1 / 2+1]1 / 2 =(1/1+1)=(1/2)

Q. The value of $x \to \infty lim (x + x + x - x)$ is

$\frac{1}{2}$

1

0

None of these

$x \to \infty lim [x + x + x - x]$
$= x \to \infty lim \frac{x + x + x - x}{x + x + x + x}$
$= x \to \infty lim \frac{x + x}{x + x + x + x}$
$= x \to \infty lim \frac{x}{x [ ( 1 + \frac{1}{x} 1 + \frac{1}{x} ) ^{1/2} + 1 ] ^{1/2}}$
$= \frac{1}{1 + 1} = \frac{1}{2}$

Q. The value of x→∞lim​(x+x+x​​​−x​) is

21​

1

0

None of these

x→∞lim​[x+x+x​​​−x​] =x→∞lim​x+x+x​​+x​​x+x+x​​−x​ =x→∞lim​x+x+x​​+x​​x+x​​​ =x→∞lim​x​[(1+x​1​1+x​1​​)1/2+1]1/2x​​ =1+11​=21​

Q. The value of $x \to \infty lim (x + x + x - x)$ is

$\frac{1}{2}$

$x \to \infty lim [x + x + x - x]$
$= x \to \infty lim \frac{x + x + x - x}{x + x + x + x}$
$= x \to \infty lim \frac{x + x}{x + x + x + x}$
$= x \to \infty lim \frac{x}{x [ ( 1 + \frac{1}{x} 1 + \frac{1}{x} ) ^{1/2} + 1 ] ^{1/2}}$
$= \frac{1}{1 + 1} = \frac{1}{2}$