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## UnkleRhaukus Group Title $\lim\limits_{n\rightarrow 0}\frac{\sin (nx)}n$ one year ago one year ago

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1. sirm3d

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

2. sirm3d

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