Question

Find \[\lim_{x \rightarrow \pi} \cot(x)\]
determine whether it is a positive or negative limit.

Answer 1

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

Answer 2

so it'd be a positive limit correct?

Answer 3

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.

Answer 4

The limit actually doesn't exist

Answer 5

Yeah haha

Answer 6

from - you get - infinity and + you get infinity

Answer 7

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

Answer 8

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

Answer 9

what if it were cot(2x) instead?

Answer 10

You should try them out yourself