## anonymous one year ago Find $\lim_{x \rightarrow \pi} \cot(x)$ determine whether it is a positive or negative limit.

1. Astrophysics

Hint: $\cot(x) = \frac{ 1 }{ \tan(x) }$

2. anonymous

so it'd be a positive limit correct?

3. 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.

4. Astrophysics

The limit actually doesn't exist

5. Astrophysics

Yeah haha

6. Astrophysics

from - you get - infinity and + you get infinity

7. Empty

Look at this graph as you approach $$\pi$$ http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphics/trig_cotan.gif

8. Astrophysics

$\lim_{x \rightarrow \pi^+} cotx = - \infty ~~~~~~ \lim_{x \rightarrow \pi ^-} cotx = \infty$

9. anonymous

what if it were cot(2x) instead?

10. Astrophysics

You should try them out yourself