Functions Question 71
Question: $ \underset{x\to \infty }{\mathop{\lim }},\frac{\sqrt{x^{2}+a^{2}}-\sqrt{x^{2}+b^{2}}}{\sqrt{x^{2}+c^{2}}-\sqrt{x^{2}+d^{2}}}= $
Options:
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
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to \infty }{\mathop{\lim }}\frac{(a^{2}-b^{2})}{(c^{2}-d^{2})},\frac{[ \sqrt{1+\frac{c^{2}}{x^{2}}}+\sqrt{1+\frac{d^{2}}{x^{2}}} ]}{[ \sqrt{1+\frac{a^{2}}{x^{2}}}+\sqrt{1+\frac{b^{2}}{x^{2}}} ]}=\frac{a^{2}-b^{2}}{c^{2}-d^{2}}. $
BETA
