Functions Question 33
Question: $ \underset{x\to 0}{\mathop{\lim }}\frac{\tan 2x-x}{3x-\sin x}= $
[IIT 1971]
Options:
A) 0
B) 1
C) ½
D) 1/3
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{\tan 2x-x}{3x-\sin x}=\underset{x\to 0}{\mathop{\lim }}{ \frac{\frac{2\tan 2x}{2x}-1}{3-\frac{\sin x}{x}} }=\frac{1}{2}. $ Aliter : Apply L-Hospital?s rule $ \underset{x\to 0}{\mathop{\lim }}\frac{\tan 2x-x}{3x-\sin x}=\underset{x\to 0}{\mathop{\lim }}\frac{2{{\sec }^{2}}2x-1}{3-\cos x}=\frac{2-1}{3-1}=\frac{1}{2}. $
BETA
