_ x 3 3 x-3 2 x-4-2 बराबर है - Vidyadip

Question

$\lim _{x \rightarrow 3} \frac{\sqrt{3 x}-3}{\sqrt{2 x-4}-\sqrt{2}}$ बराबर है

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Answer

b
Let $A = \,\,\,\mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {3x} - 3}}{{\sqrt {2x - 4} - \sqrt 2 }}$

Rationalise

$ \Rightarrow A = \,\,\,\mathop {\lim }\limits_{x \to 3} \frac{{\left( {3x - 9} \right) \times \left( {2x - 4 + \sqrt 2 } \right)}}{{\left\{ {\left( {2x - 4 - 2} \right)} \right\} \times \left( {\sqrt {3x} + 3} \right)}}$

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

$ = \frac{3}{2} \times \frac{{2\sqrt 2 }}{6} = \frac{1}{{\sqrt 2 }}$

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