MCQ
$\mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {3x} - 3}}{{\sqrt {2x - 4} - \sqrt 2 }}$ is equal to
- A$\sqrt 3 $
- ✓$\frac{1}{{\sqrt 2 }}$
- C$\frac{{\sqrt 3 }}{2}$
- D$\frac{1}{{2\sqrt 2 }}$
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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