lim x → 0 sin x n x n

limx→0sin xnxn It is of the form 00 Let y=xn⇒limx→0=limy→0⇒limy→0sin yy⇒1 ∵limx→0sin xx=1

$\lim_{x \to 0} \frac{\sin x^{n}}{x^{n}}$

\lim_{x \to 0} \frac{\sin x^{n}}{x^{n}}

It is of the form

(\frac{0}{0})

Let y = x^{n} \Rightarrow \lim_{x \to 0} = \lim_{y \to 0} \Rightarrow \lim_{y \to 0} \frac{\sin y}{y} \Rightarrow 1 \{∵ \lim_{x \to 0} \frac{\sin x}{x} = 1\}