A) 0
B) \[\infty \]
C) 2
D) \[\frac{1}{2}\]
Correct Answer: C
Solution :
On rationalization \[\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{4x}{(\sqrt{{{x}^{2}}+8x+3}+\sqrt{{{x}^{2}}+4x+3}}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{4}{\left( \sqrt{1+\frac{8}{x}+\frac{3}{{{x}^{2}}}}+\sqrt{1+\frac{4}{x}+\frac{3}{{{x}^{2}}}} \right)}=2\].
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