Functions Question 198
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{\sqrt{1-x^{2}}-\sqrt{1+x^{2}}}{x^{2}} $ is equal to
[MP PET 1999]
Options:
A) 1
B) ?1
C) ?2
D) 0
Show Answer
Answer:
Correct Answer: B
Solution:
On rationalising, the given limit $ =\underset{x\to 0}{\mathop{\lim }}\frac{(1-x^{2}-1-x^{2})}{x^{2},(\sqrt{1-x^{2}}+\sqrt{1+x^{2})}} $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{-2}{\sqrt{1-x^{2}}+\sqrt{1+x^{2}}}=\frac{-2}{1+1}=-1 $
BETA
