Limit Continuity and Differentiability 1 Question 12
13. If $\lim _{x \rightarrow 0} \frac{{(a-n) n x-\tan x} \sin n x}{x^{2}}=0$, where $n$ is non-zero real number, then $a$ is equal to
(a) 0
(b) $\frac{n+1}{n}$
(c) $n$
(d) $n+\frac{1}{n}$
(2012)
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Answer:
Correct Answer: 13. (d)
Solution:
- For $x \in R, \lim _{x \rightarrow \infty} \frac{x-3}{x+2}^{x}=\lim _{x \rightarrow \infty} \frac{(1-3 / x)^{x}}{(1+2 / x)^{x}}=\frac{e^{-3}}{e^{2}}=e^{-5}$
