The correct option is A 2 lim_x→ 1x+1/√(x^2+3) 2 =lim _ x→ 1 (x+1)(√( x^ 2 +3 ) +2) / x^ 2 1 =lim _ x→ 1 (√( x^ 2 +3 ) +2) / x 1 ...

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Properties Derived from Trigonometric Identities

limx→ -1x+1/√...

Question

$lim x \to - 1 \frac{x + 1}{\sqrt{x^{2} + 3} - 2}$ =

- 2

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\frac{1}{2}

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2

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0

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Solution

The correct option is A $- 2$
$lim x \to - 1 \frac{x + 1}{\sqrt{x^{2} + 3} - 2}$
$= {lim}_{x \to - 1} \frac{(x + 1) (\sqrt{x^{2} + 3} + 2)}{x^{2} - 1}$
$= {lim}_{x \to - 1} \frac{(\sqrt{x^{2} + 3} + 2)}{x - 1}$
$= \frac{4}{- 2} = - 2$

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