Evaluate - x- 0lim-3x-12-x2x-3-9-5x3

The correct option is A 2/3 x→ 0lim√(3)x √(12 x)2x 3(√(9 5x3)) .Substitute x=0 =√(3)(0) √(12 0)2(0) 3(√(9 5(0)3)) = √(12) 3√(93) = ...

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Algebra of Limits

Evaluate : ...

Question

Evaluate :
$lim x \to 0 \frac{\sqrt{3} x - \sqrt{12 - x}}{2 x - 3 (\sqrt{\frac{9 - 5 x}{3}})}$

2 / 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5 / 12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 / 13

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 / 39

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 / 3$
$lim x \to 0 \frac{\sqrt{3} x - \sqrt{12 - x}}{2 x - 3 (\sqrt{\frac{9 - 5 x}{3}})}$ .

Substitute $x = 0$
$= \frac{\sqrt{3} (0) - \sqrt{12 - 0}}{2 (0) - 3 ⎛ ⎝ \sqrt{\frac{9 - 5 (0)}{3}} ⎞ ⎠}$

$= \frac{- \sqrt{12}}{- 3 \sqrt{\frac{9}{3}}}$

$= \frac{\sqrt{12}}{3 \times \frac{3}{\sqrt{3}}}$

$= \frac{(2 \sqrt{3}) \times \sqrt{3}}{9}$

$= \frac{2 \times 3}{9}$

$lim x \to 0 \frac{\sqrt{3} x - \sqrt{12 - x}}{2 x - 3 (\sqrt{\frac{9 - 5 x}{3}})} = \frac{2}{3}$

Option A is correct.

Suggest Corrections

Similar questions

Q. If

x = 15^{0}

, evaluate:

12 sin 3 x cos 3 x + 5 tan (2 x + 15^{0}) - 3 {cot}^{2} 3 x

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

Q. Evaluate:

{lim}_{x \to \sqrt{2}} \frac{x^{9} - {3 x}^{8} + x^{6} - {9 x}^{4} - {4 x}^{2} - 16 x + 84}{x^{5} - {3 x}^{4} - 4 x + 12}

Q. If

x =

20^{\circ}

, evaluate :

12 sin \frac{3 x}{2} cos 3 x + 5 tan (2 x + 5^{\circ}) - 3 {cot}^{2} 3 x

Q. Evaluate for

x

3 (x - 3) - 2 (x - 1) = 5 (x - 5)

Join BYJU'S Learning Program

Evaluate : limx→0√3x−√12−x2x−3(√9−5x3)

The correct option is A 2/3limx→0√3x−√12−x2x−3(√9−5x3).Substitute x=0=√3(0)−√12−02(0)−3⎛⎝√9−5(0)3⎞⎠=−√12−3√93=√123×3√3=(2√3)×√39=2×39limx→0√3x−√12−x2x−3(√9−5x3)=23Option A is correct.

Evaluate :
$lim x \to 0 \frac{\sqrt{3} x - \sqrt{12 - x}}{2 x - 3 (\sqrt{\frac{9 - 5 x}{3}})}$