The correct option is A 2 #160;lim _ x⟶ 1 x ^ 2 1 x 1 #160; #160; #160;=lim _ x⟶ #160;1 x ^ 2 1 ^ 2 x ^ 1 1 ^ 1 #160; #160; ...

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Theorems for Continuity

x→ 1limx2-1/x...

Question

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

0

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2

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1

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Solution

The correct option is A $2$
${lim}_{x ⟶ 1} \frac{x^{2} - 1}{x - 1} = {lim}_{x ⟶ 1} \frac{x^{2} - 1^{2}}{x^{1} - 1^{1}}$

$= 2 \times 1^{2 - 1}$
$= 2$ .....( since ${lim}_{x \to a} \frac{x^{m} - a^{m}}{x^{n} - a^{n}} = \frac{m}{n} a^{m - n})$

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