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Question-108997




Question Number 108997 by 150505R last updated on 20/Aug/20
Answered by Dwaipayan Shikari last updated on 20/Aug/20
lim_(n→∞) sin(n^2 π((1+(3/n)+(4/n^2 )−(5/n^3 )))^(1/3)  )  lim_(n→∞) sin(n^2 π)=f(x)  −1≤f(x)≤1
$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{sin}\left({n}^{\mathrm{2}} \pi\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{3}}{{n}}+\frac{\mathrm{4}}{{n}^{\mathrm{2}} }−\frac{\mathrm{5}}{{n}^{\mathrm{3}} }}\:\right) \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{sin}\left({n}^{\mathrm{2}} \pi\right)={f}\left({x}\right) \\ $$$$−\mathrm{1}\leqslant{f}\left({x}\right)\leqslant\mathrm{1} \\ $$$$ \\ $$

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