Question

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Answer 1

Step-by-step explanation:

We have,

$\lim _{x \rarr1} \frac{ {x}^{2} + \sqrt{x + 3} - 3 }{ {x}^{2} - 1 }$

$= \lim _{x \rarr1} \frac{2x + \frac{1}{2 \sqrt{x + 3} } - 0}{2x} \\ ......(using \: \: l \: hospitals \: \: rule)$

$= \frac{2 + \frac{1}{2 \sqrt{1 + 3} } }{2}$

$= \frac{2 + \frac{1}{4} }{2}$

$= 1 + \frac{1}{8}$

$= \frac{9}{8}$