anonymous
  • anonymous
Find the limit: lim as x approaches 0 of cos(1/x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
DNE
SolomonZelman
  • SolomonZelman
\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}\)
SolomonZelman
  • SolomonZelman
That, does not exist

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anonymous
  • anonymous
@pgpilot326 can you explain?
anonymous
  • anonymous
@solomonzelman why?
Zale101
  • Zale101
If you sub in x=0, you'll get a 0 in the denominator which is undefined.
SolomonZelman
  • SolomonZelman
\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}=\cos\left(\displaystyle \lim_{x \rightarrow ~0}\frac{1}{x}\right)\)
anonymous
  • anonymous
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)
SolomonZelman
  • SolomonZelman
yes, that is equivalent of \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}=\cos\left(\displaystyle \lim_{x \rightarrow ~0}\frac{1}{x}\right)=\cos\left(\displaystyle \lim_{x \rightarrow ~\infty }x\right)\)
SolomonZelman
  • SolomonZelman
So it will alternate between 1 and -1
SolomonZelman
  • SolomonZelman
|dw:1441658924817:dw|

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