Functions Question 276
Question: If $ \underset{x\to 0}{\mathop{\lim }},\frac{
[(a-n),nx-\tan x]\sin nx}{x^{2}}=0, $ where n is non zero real number, then a is equal to [IIT Screening 2003]
Options:
A) 0
B) $ \frac{n+1}{n} $
C) n
D) $ n+\frac{1}{n} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 0}{\mathop{\lim }},n\frac{\sin nx}{nx}.\underset{x\to 0}{\mathop{\lim }},( (a-n)n-\frac{\tan x}{x} )=0 $
Þ $ n((a-n)n-1)=0\Rightarrow (a-n)n=1\Rightarrow a=n+\frac{1}{n} $ .
BETA
