A) \[\frac{{{a}^{2}}-{{b}^{2}}}{{{c}^{2}}-{{d}^{2}}}\]
B) \[\frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}-{{d}^{2}}}\]
C) \[\frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}}\]
D) None of these
Correct Answer: A
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{({{a}^{2}}-{{b}^{2}})}{({{c}^{2}}-{{d}^{2}})}\,\frac{\left[ \sqrt{1+\frac{{{c}^{2}}}{{{x}^{2}}}}+\sqrt{1+\frac{{{d}^{2}}}{{{x}^{2}}}} \right]}{\left[ \sqrt{1+\frac{{{a}^{2}}}{{{x}^{2}}}}+\sqrt{1+\frac{{{b}^{2}}}{{{x}^{2}}}} \right]}=\frac{{{a}^{2}}-{{b}^{2}}}{{{c}^{2}}-{{d}^{2}}}.\]
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