12. limits — ગણિત ધોરણ 11 સાયન્સ — Question

so that $x \to \infty \,\, \Rightarrow \,y \to 0$

$\therefore \,\mathop {\lim }\limits_{x \to \infty } \,\left( {\frac{{\sin x}}{x}} \right) = \mathop {\lim }\limits_{y \to 0} \,\left( {y.\sin \frac{1}{y}} \right)$

$= \mathop {\lim }\limits_{y \to 0} \,y \times \mathop {\lim }\limits_{y \to 0} \,\sin \frac{1}{y} = 0 \times ... = 0$