Functions Question 687
Question: $ \underset{x\to a}{\mathop{\lim }},\frac{\sqrt{3x-a}-\sqrt{x+a}}{x-a}= $
Options:
A) $ \sqrt{2}a $
B) $ 1/\sqrt{2a} $
C) 2a
D) $ 1/2a $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to a}{\mathop{\lim }}\frac{\sqrt{3x-a}-\sqrt{x+a}}{x-a} $ $ =\underset{x\to a}{\mathop{\lim }}\frac{\sqrt{3x-a}-\sqrt{x+a}}{(x-a)}\times \frac{\sqrt{3x-a}+\sqrt{x+a}}{\sqrt{3x-a}+\sqrt{x+a}} $ $ =\frac{2}{2\sqrt{2a}}=\frac{1}{\sqrt{2a}} $ Aliter : Apply L-Hospital?s rule $ \underset{x\to a}{\mathop{\lim }}\frac{\sqrt{3x-a}-\sqrt{x+a}}{x-a}=\underset{x\to a}{\mathop{\lim }}\frac{3}{2,\sqrt{3x-a}}-\frac{1}{2,\sqrt{x+a}} $ $ =\frac{3}{2\sqrt{2a}}-\frac{1}{2\sqrt{2a}}=\frac{1}{\sqrt{2a}}. $
BETA
