Differentiation Question 170
Question: If $ \underset{x\to 0}{\mathop{\lim }}\frac{(sinnx)[(a-n)nx-tanx]}{x^{2}}=0, $ then the value of a
Options:
A) $ \frac{1}{n} $
B) $ n-\frac{1}{n} $
C) $ n+\frac{1}{n} $
D) None
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let $ \underset{x\to 0}{\mathop{\lim }}\frac{(sinnx)[(a-n)nx-tanx]}{x^{2}}=0 $
$ \Rightarrow \underset{x\to 0}{\mathop{\lim }}\frac{( nx-\frac{n^{3}x^{3}}{3!} )[ n(a-n)x-{ x+\frac{x^{3}}{3}+… } ]}{x^{2}}=0 $ (By suing expansion of sin x and tan x)
$ \Rightarrow n^{2}(a-n)-n=0\Rightarrow an-n^{2}-1=0 $
$ \Rightarrow a=\frac{n^{2}+1}{n}=n+\frac{1}{n} $
BETA
