Infinite limits with cot?

1. Apr 10, 2012

shocklightnin

1. The problem statement, all variables and given/known data
lim x->pi- cot(x)

2. Relevant equations
cot(x) = cos(x)/sin(x)

3. The attempt at a solution

so substituting pi into:
cot(pi) = cos(pi)/sin(pi)
= -1/0
so you have a negative over 0, approaching from the -ve side of pi wouldn't it be +infinity? why is it -infinity?

additionally this confuses me because a previous question I was working went like:

1)lim x->-3+ (x+2)/(x+3) = - infinity
2)lim x->-3- (x+2)/(x+3) = + infinity
when substituting in 3, one would get a -ve int/0.
so i thought you found out whether it is +ve or -ve infinity by multiplying signs.
1) -3+ so take + times - (from -ve int) = -ve ...and you get -ve infinity
2) -3- so take - times - (from -ve int) = +ve ...and you get +ve infinity

but that was the way a friend showed me, its worked for all the questions up until the cotx one. any help in understanding is much appreciated, thanks.

2. Apr 10, 2012

SammyS

Staff Emeritus
What is the sign of sin(x) when x is a little less than π ?

3. Apr 10, 2012

shocklightnin

positive..?

4. Apr 10, 2012

Mentallic

Right, so it should be $$\frac{-1}{0^+}$$ because we're looking at $\sin(\pi ^-)$

5. Apr 11, 2012

shocklightnin

ooh right right! so thats why its -ve infinity. ah thanks, got it now :P