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UnkleRhaukus

  • 3 years ago

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

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  1. sirm3d
    • 3 years ago
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    \[\large \lim_{n \rightarrow 0}\frac{ \sin nx }{ n }=\lim_{n \rightarrow 0}\frac{ x(\sin nx) }{ nx }=x(1)=x\]

  2. sirm3d
    • 3 years ago
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    you can also apply L'Hopital's Rule on the function, the variable of differentiation is n. \[\large \lim_{n \rightarrow 0}\frac{ \sin nx }{ n }=\lim_{n \rightarrow 0}\frac{ x \cos nx }{ 1 }=x\]

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