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) = ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Limits

Evaluate : ...

Question

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

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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.

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