Functions Question 173
Question: $ \underset{x\to \infty }{\mathop{\lim }},[ \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x} ] $ is equal to
Options:
A) 0
B) $ \frac{1}{2} $
C) $ \frac{1}{p}-\frac{1}{p-1} $
D) $ e^{4} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to \infty }{\mathop{\lim }}[ \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x} ]=\underset{x\to \infty }{\mathop{\lim }},\frac{x+\sqrt{x+\sqrt{x}}-x}{\sqrt{x+\sqrt{x+\sqrt{x}}}+\sqrt{x}} $ $ =\underset{x\to \infty }{\mathop{\lim }},\frac{\sqrt{x+\sqrt{x}}}{\sqrt{x+\sqrt{x+\sqrt{x}}}+\sqrt{x}}=\underset{x\to \infty }{\mathop{\lim }}\frac{\sqrt{1+{x^{-1/2}}}}{\sqrt{1+\sqrt{{x^{-1}}+{x^{-3/2}}}}+1}=\frac{1}{2} $ .
BETA
