anonymous
  • anonymous
Find \[\lim_{x \rightarrow \pi} \cot(x)\] determine whether it is a positive or negative limit.
Mathematics
jamiebookeater
  • jamiebookeater
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Astrophysics
  • Astrophysics
Hint: \[\cot(x) = \frac{ 1 }{ \tan(x) }\]
anonymous
  • anonymous
so it'd be a positive limit correct?
Empty
  • Empty
The limit doesn't exist, because if you approach from the left it will be negative and if you approach from the right it will be positive.

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Astrophysics
  • Astrophysics
The limit actually doesn't exist
Astrophysics
  • Astrophysics
Yeah haha
Astrophysics
  • Astrophysics
from - you get - infinity and + you get infinity
Empty
  • Empty
Look at this graph as you approach \(\pi\) http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphics/trig_cotan.gif
Astrophysics
  • Astrophysics
\[\lim_{x \rightarrow \pi^+} cotx = - \infty ~~~~~~ \lim_{x \rightarrow \pi ^-} cotx = \infty \]
anonymous
  • anonymous
what if it were cot(2x) instead?
Astrophysics
  • Astrophysics
You should try them out yourself

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