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Question Number 91930 by Ozoda last updated on 03/May/20

$$\underset{x\to 0}{\lim cos}\frac{1}{x}=$$

Commented by mr W last updated on 03/May/20

$$whenx\to 0,\frac{1}{x}\to \mathrm{\infty },\cos \frac{1}{x}{doesn}^{\prime }t$$$$approachacertainvalue,therefore$$$$\underset{x\to 0}{\lim }\cos \frac{1}{x}{doesn}^{\prime }texist.$$

Commented by turbo msup by abdo last updated on 03/May/20

$$ifthislimitexistwemusthsve$$$$ofallsequence\left(x_n\right)\to 0limcos\left(x_n\right)$$$$existlet{x}_n=\frac{1}{n\pi }wehave{x}_n\to 0sndd$$$$cos\left(x_n\right)=cos\left(n\pi \right)={(-1)}^{n}this$$$$sequencehaventanylimit\to$$$${lim}_{x\to 0}cosxdontexist..$$

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