displaystyle limx→3 (√3x - 3/√2x - 4 - √2) is equal to :

Question

displaystyle limx→3 (√3x - 3/√2x - 4 - √2) is equal to : (A) √3 (B) (1/√2) (C) (√3/2) (D) (1/2√2)

Tardigrade Admin · Accepted Answer

displaystyle limx → 3 (√3x-3/√2x-4-√2) Rationalize displaystyle limx → 3 ((3x-9)×(√2x-4+4√2)/ (2x-4)-2 ×(√3x+3)) = displaystyle limx → 3 (3(x-3)/2(x-3))×(√2x-4+√2/(√3x+3)) = (3/2)×(2√2/6) = (1/√2)

Q. $x \to 3 lim \frac{3 x - 3}{2 x - 4 - 2}$ is equal to :

$3$

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{1}{2 2}$

$x \to 3 lim$ $\frac{3 x - 3}{2 x - 4 - 2}$
Rationalize
$x \to 3 lim$ $\frac{( 3 x - 9 ) \times ( 2 x - 4 + 4 2 )}{{ ( 2 x - 4 ) - 2 } \times ( 3 x + 3 )}$
$= x \to 3 lim$ $\frac{3 ( x - 3 )}{2 ( x - 3 )} \times \frac{2 x - 4 + 2}{( 3 x + 3 )}$
$= \frac{3}{2} \times \frac{2 2}{6} = \frac{1}{2}$

Q. x→3lim​2x−4​−2​3x​−3​ is equal to :

3​

2​1​

23​​

22​1​

x→3lim​ 2x−4​−2​3x​−3​ Rationalize x→3lim​ {(2x−4)−2}×(3x+3​)(3x−9)×(2x−4​+42​)​ =x→3lim​ 2(x−3)3(x−3)​×(3x​+3)2x−4​+2​​ =23​×622​​=2​1​

Q. $x \to 3 lim \frac{3 x - 3}{2 x - 4 - 2}$ is equal to :

$3$

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{1}{2 2}$

$x \to 3 lim$ $\frac{3 x - 3}{2 x - 4 - 2}$
Rationalize
$x \to 3 lim$ $\frac{( 3 x - 9 ) \times ( 2 x - 4 + 4 2 )}{{ ( 2 x - 4 ) - 2 } \times ( 3 x + 3 )}$
$= x \to 3 lim$ $\frac{3 ( x - 3 )}{2 ( x - 3 )} \times \frac{2 x - 4 + 2}{( 3 x + 3 )}$
$= \frac{3}{2} \times \frac{2 2}{6} = \frac{1}{2}$