Functions Question 195
Question: $ \underset{x\to \infty }{\mathop{\lim }},(\sqrt{x^{2}+8x+3}-\sqrt{x^{2}+4x+3})= $
[MP PET 1997]
Options:
A) 0
B) $ \infty $
C) 2
D) $ \frac{1}{2} $
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Answer:
Correct Answer: C
Solution:
On rationalization $ \underset{x\to \infty }{\mathop{\lim }}\frac{4x}{(\sqrt{x^{2}+8x+3}+\sqrt{x^{2}+4x+3}} $ $ =\underset{x\to \infty }{\mathop{\lim }}\frac{4}{( \sqrt{1+\frac{8}{x}+\frac{3}{x^{2}}}+\sqrt{1+\frac{4}{x}+\frac{3}{x^{2}}} )}=2 $ .
BETA
