Question

\[\lim\limits_{n\rightarrow 0}\frac{\sin (nx)}n\]

Answer 1

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

Answer 2

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