Functions Question 94
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{\sqrt{1+x}-\sqrt{1-x}}{{{\sin }^{-1}}x}= $
[AI CBSE 1989, 1990; DSSE 1989]
Options:
2
1
?1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ {{\sin }^{-1}}x=y\Rightarrow x=\sin y $ So $ \underset{y\to 0}{\mathop{\lim }},\frac{\sqrt{1+\sin y}-\sqrt{1-\sin y}}{y} $ $ (\because ,x\to 0\Rightarrow y\to \frac{\pi}{2}) $ $ \underset{x\to 0}{\mathop{\lim }},\frac{\log (3+x)-\log (3-x)}{x}=k $ $ $ =1 Aliter : Apply L’Hospital’s rule.
BETA
