Question

If ${lim}_{x\to 0}\frac{x^n{\sin }^{n}x}{x^n-{\sin }^{n}x}$ is non-zero finite, then n is equal to

• A. 1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is D none of these

${lim}_{x\to 0}\frac{x^n{\sin }^{n}x}{x^n-{\sin }^{n}x}Dividedby{x}^n{lim}_{x\to 0}\frac{\frac{x^n{\sin }^{n}x}{x^n}}{\frac{x^n}{x^n}-\frac{{\sin }^{n}x}{x^n}}$
So, for $n=0$, only it will be define.