Question

The integer ${}^{\prime }{n}^{\prime }$ for which $\underset{x\to 0}{lim}\frac{\cos 2x-1}{x^n}$ is a finite non-zero number is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$\begin{array}{c}\underset{x\to 0}{lim}\frac{\cos 2x-1}{x^n}=\underset{x\to 0}{lim}\frac{-2{\sin }^{2}x}{x^n}\\ at,n=2\\ \underset{x\to 0}{lim}\frac{-2{\sin }^{2}x}{x^2}=-2\end{array}$

which is a finite non-zero number