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# Answer on Calculus Question for lalu

Question #2204
Evaluate lim x-&gt;5 (sqrt(5x)-5)/(sqrt(2x-4)-sqrt(6).
Since we have ambiguity of 0/0, we can use l&#039;Hopital rule:
&lt;img src=&quot;/cgi-bin/mimetex.cgi?%5Clim_%7Bx%20%5Cto%201%7D%20%5Cfrac%7B%28%5Csqrt%7B5x%7D%20-5%29%27%7D%7B%28%5Csqrt%7B2x-4%7D-%20%5Csqrt%7B6%7D%29%27%7D%20=%20%5Clim_%7Bx%20%5Cto%201%7D%20%5Cfrac%7B5/%282%5Csqrt%7B5x%7D%29%7D%7B2/%282%5Csqrt%7B2x-4%7D%29%7D%20=%20%5Clim_%7Bx%20%5Cto%201%7D%20%5Cfrac%7B5%20%5Csqrt%7B2x-4%7D%7D%7B2%5Csqrt%7B5x%7D%7D%20=%20%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B2%7D&quot; title=&quot;\lim_{x \to 1} \frac{(\sqrt{5x} -5)&#039;}{(\sqrt{2x-4}- \sqrt{6})&#039;} = \lim_{x \to 1} \frac{5/(2\sqrt{5x})}{2/(2\sqrt{2x-4})} = \lim_{x \to 1} \frac{5 \sqrt{2x-4}}{2\sqrt{5x}} = \frac{\sqrt{6}}{2}&quot;&gt;

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