<span class="math-tex">\(\lim_{x \rightarrow 3} \frac {\sqrt {3x} - 3}{\sqrt {2x - 4} - \sqrt 2}\)</span> is equal to
This is a \(\frac{0}{0}\) form. Apply L'Hôpital's rule:
Numerator: \(\frac{d}{dx}\sqrt{3x} = \frac{3}{2\sqrt{3x}}\), which is \(\frac{3}{6} = \frac{1}{2}\) at x = 3.
Denominator: \(\frac{d}{dx}\sqrt{2x - 4} = \frac{1}{\sqrt{2x - 4}}\), which is \(\frac{1}{\sqrt{2}}\) at x = 3.
Limit = \(\frac{1/2}{1/\sqrt{2}} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}\)
Answer: (D)
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