Question

$\underset{x\to 0}{\lim }\frac{\sin x^n}{x^n}$

Answer 1

$\underset{x\to 0}{\lim }\frac{\sin x^n}{x^n}$

It is of the form $\left(\frac{0}{0}\right)$.

$$\begin{gathered} \mathrm{Let}y=x^n \\ \Rightarrow \underset{x\to 0}{\lim }=\underset{y\to 0}{\lim } \\ \Rightarrow \underset{y\to 0}{\lim }\frac{\sin y}{y} \\ \Rightarrow 1\left\{\because \underset{x\to 0}{\lim }\frac{\sin x}{x}=1\right\} \end{gathered}$$