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Question Number 195021 by tri26112004 last updated on 22/Jul/23

$$\underset{x\to 0}{\lim }\frac{x-sinx}{x^n}=¿(n\in N^{\ast })$$

Answered by MM42 last updated on 22/Jul/23

$$ifx\to 0\Rightarrow x-sinx\sim \frac{1}{6}{x}^3$$$$\Rightarrow ifn<3\Rightarrow lim=0$$$$ifn=3\Rightarrow lim=\frac{1}{6}$$$$ifn>3\Rightarrow lim=\mathrm{\infty }$$

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