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Question Number 62180 by Mikael last updated on 17/Jun/19

$$\underset{x\to \mathrm{\infty }}{lim}\frac{senx}{x}$$

Commented by maxmathsup by imad last updated on 17/Jun/19

$$ifyoumeansinxwehave\mid sinx\mid ⩽1\Rightarrow \mid \frac{sinx}{x}\mid ⩽\frac{1}{\mid x\mid }forallx\ne 0but$$$${lim}_{x\to \mathrm{\infty }}\frac{1}{\mid x\mid }=0\Rightarrow {lim}_{x\to \mathrm{\infty }}\frac{sinx}{x}=0$$

Commented by Tony Lin last updated on 17/Jun/19

$$\mathrm{\forall }\epsilon >0\Rightarrow 0⩽\mid \frac{senx}{x}\mid ⩽\mid \frac{1}{x}\mid \mathrm{\forall }x⩾\frac{1}{\epsilon }$$$$\because \underset{x\to \mathrm{\infty }}{\lim 0}=0and\underset{x\to \mathrm{\infty }}{\lim }\frac{1}{x}=0$$$$\Rightarrow \underset{x\to \mathrm{\infty }}{\lim }\frac{senx}{x}=0\left(squeezetheoreom\right)$$

Commented by Mikael last updated on 17/Jun/19

$$thankyouSir$$

Commented by malwaan last updated on 18/Jun/19

$$sen?$$$$\mathit{s}\mathit{e}\mathit{c}\mathit{o}\mathit{r}\mathit{s}\mathit{i}\mathit{n}?$$

Commented by Mikael last updated on 18/Jun/19

$$sinSir.$$

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