First slide

Introduction to limits

Question

$If lim_{x \to 0} \frac{{(a−n)nx−tan⁡x}sin⁡n x}{x^{2}} = 0, where n is a non-zero real number, then 'a'$

Moderate

A

0
B

$\frac{n + 1}{n}$
C

$n$
D

$n + \frac{1}{n}$

Solution

$\begin{array}{l} \lim_{x \to 0} \{(a - n) n - \frac{\tan x}{x}\} \frac{\sin n x}{x} = 0 \\ \Rightarrow n [(a - n) n - 1] = 0 \\ \Rightarrow (a - n) n = 1 \\ \Rightarrow a = n + \frac{1}{n} \end{array}$

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