Functions Question 117
Question: $ \underset{x\to \pi /4}{\mathop{\lim }},\frac{\sqrt{2}\cos x-1}{\cot x-1}= $
[BIT Ranchi 1989; IIT 1990]
Options:
A) $ \frac{1}{\sqrt{2}} $
B) $ \frac{1}{2} $
C) $ \frac{1}{2\sqrt{2}} $
D) 1
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Answer:
Correct Answer: B
Solution:
$ \underset{x\to \pi /4}{\mathop{\lim }}\frac{(\sqrt{2}-\sec x),\cos x,(1+\cot x)}{\cot x,[2-{{\sec }^{2}}x]} $ $ =\underset{x\to \pi /4}{\mathop{\lim }},\frac{\sin x,(1+\cot x)}{(\sqrt{2}+\sec x)}=\frac{\frac{1}{\sqrt{2}}(2)}{\sqrt{2}+\sqrt{2}}=\frac{1}{2}. $ Aliter : Apply L-Hospital?s rule.
BETA
