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Integration by Partial Fractions

Evaluate li...

Question

Evaluate $lim x \to - 2 \frac{x^{2} - 1}{2 x + 4}$ .

A

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B

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C

2

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D

\infty

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Solution

The correct option is C $\infty$
Consider, $lim x \to - 2^{+} \frac{x^{2} - 1}{2 x + 4}$

Substitute $x = - 2 + h$

$⟹ h \to 0 as x \to - 2$

$⟹ lim x \to - 2^{+} \frac{x^{2} - 1}{2 x + 4}$ $= lim h \to 0 \frac{(h - 2)^{2} - 1}{2 (h - 2) + 4}$
$= lim h \to 0 \frac{h^{2} - 4 h + 3}{2 h}$
$= \infty$

Hence, $lim x \to - 2^{+} \frac{x^{2} - 1}{2 x + 4} = \infty$

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