Functions Question 52
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{\sin 2x+\sin 6x}{\sin 5x-\sin 3x}= $
[AI CBSE 1988; AISSE 1988]
Options:
A) ½
B) 1/4
C) 2
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 0}{\mathop{\lim }},\frac{2\sin 4x\cos 2x}{2\sin x\cos 4x}=\underset{x\to 0}{\mathop{\lim }},4( \frac{\sin 4x}{4x} ),( \frac{x}{\sin x} )\frac{\cos 2x}{\cos 4x}=4 $ . Aliter : $ \underset{x\to 0}{\mathop{\lim }},\frac{\frac{2\sin 2x}{2x}+\frac{6\sin 6x}{6x}}{\frac{5\sin 5x}{5x}-\frac{3\sin 3x}{3x}}=\frac{2+6}{5-3}=4. $
BETA
