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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
Question
$\mathop {\lim }\limits_{x \to 3} \left\{ {\frac{{x - 3}}{{\sqrt {x - 2} - \sqrt {4 - x} }}} \right\} = $
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Answer

a
(a) $\mathop {\lim }\limits_{x \to 3} \,\left\{ {\frac{{x - 3}}{{\sqrt {x - 2} - \sqrt {4 - x} }}} \right\} = \mathop {\lim }\limits_{x \to 3} \,\frac{{(x - 3)\,\left\{ {\sqrt {x - 2} + \sqrt {4 - x} } \right\}}}{{2\,(x - 3)}} = 1$.

Aliter : Apply  $ L-$ Hospital’s rule.

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