Functions Question 167
Question: The value of $ \underset{x\to \infty }{\mathop{\lim }},\sqrt{a^{2}x^{2}+ax+1}-\sqrt{a^{2}x^{2}+1} $ is
Options:
A) $ \frac{1}{2} $
B) 1
C) $ 2 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to \infty }{\mathop{\lim }}\sqrt{a^{2}x^{2}+ax+1}-\sqrt{a^{2}x^{2}+1} $ $ =\underset{x\to \infty }{\mathop{\lim }}\frac{ax}{,\sqrt{a^{2}x^{2}+ax+1}+\sqrt{a^{2}x^{2}+1}} $ $ =\underset{x\to \infty }{\mathop{\lim }}\frac{a}{,\sqrt{a^{2}+\frac{a}{x}+\frac{1}{x^{2}}}+\sqrt{a^{2}+\frac{1}{x^{2}}}}=\frac{a}{2a}=\frac{1}{2} $ .
BETA
