Question

$\underset{x\to 0}{lim}\frac{\sin \left(x^n\right)}{(\sin x{)}^m}(m$, $n\in N)=0$, lf

• A. $m>n$
• B. $m=n$
• C. $n>m$
• D. Always

Answer 1

Answer: (C)

$n>m$

The given limit can be written in the form of,
${lim}_{x\to 0}\frac{\sin x^n}{x^n}\times {\left(\frac{x}{\sin x}\right)}^m\times x^{n-m}$
Using the property of limits,
This limit will exist and equal to $0$ only if $n>m$.
Hence, option 'C' is correct.