Find the limit: lim as x approaches 0 of cos(1/x)

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Find the limit: lim as x approaches 0 of cos(1/x)

Mathematics
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DNE
\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}\)
That, does not exist

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Other answers:

@pgpilot326 can you explain?
If you sub in x=0, you'll get a 0 in the denominator which is undefined.
\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}=\cos\left(\displaystyle \lim_{x \rightarrow ~0}\frac{1}{x}\right)\)
as x approaches 0, 1/x approaches infinity. cos will cycles through all of it's values and not settle on a single value (which it would need to do in order for the limit to exist)
yes, that is equivalent of \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}=\cos\left(\displaystyle \lim_{x \rightarrow ~0}\frac{1}{x}\right)=\cos\left(\displaystyle \lim_{x \rightarrow ~\infty }x\right)\)
So it will alternate between 1 and -1
|dw:1441658924817:dw|

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