The correct option is C 1/6 lim_x→ 43 √(5+x)/x 4 =lim_x→ 43 √(5+x)/x 4×3+√(5+x)/3+√(5+x) =lim_x→ 49 (5+x)/x 4×1/3+√(5+x) = lim_x→ 41/ ...

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Rationalization Method to Remove Indeterminate Form

limx→ 43-√5+x...

Question

$lim x \to 4 \frac{3 - \sqrt{5 + x}}{x - 4}$ =

- \frac{1}{5}

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\frac{1}{6}

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\frac{1}{5}

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- \frac{1}{6}

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Solution

The correct option is C $- \frac{1}{6}$
$lim x \to 4 \frac{3 - \sqrt{5 + x}}{x - 4}$
$= lim x \to 4 \frac{3 - \sqrt{5 + x}}{x - 4} \times \frac{3 + \sqrt{5 + x}}{3 + \sqrt{5 + x}}$
$= lim x \to 4 \frac{9 - (5 + x)}{x - 4} \times \frac{1}{3 + \sqrt{5 + x}}$
$= - lim x \to 4 \frac{1}{3 + \sqrt{5 + x}} = - \frac{1}{6}$

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