## UnkleRhaukus 3 years ago $\lim\limits_{n\rightarrow 0}\frac{\sin (nx)}n$

1. anonymous

$\large \lim_{n \rightarrow 0}\frac{ \sin nx }{ n }=\lim_{n \rightarrow 0}\frac{ x(\sin nx) }{ nx }=x(1)=x$

2. anonymous

you can also apply L'Hopital's Rule on the function, the variable of differentiation is n. $\large \lim_{n \rightarrow 0}\frac{ \sin nx }{ n }=\lim_{n \rightarrow 0}\frac{ x \cos nx }{ 1 }=x$