1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Infinite limits with cot?

  1. Apr 10, 2012 #1
    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. jcsd
  3. Apr 10, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    What is the sign of sin(x) when x is a little less than π ?
  4. Apr 10, 2012 #3
  5. Apr 10, 2012 #4


    User Avatar
    Homework Helper

    Right, so it should be [tex]\frac{-1}{0^+}[/tex] because we're looking at [itex]\sin(\pi ^-)[/itex]
  6. Apr 11, 2012 #5
    ooh right right! so thats why its -ve infinity. ah thanks, got it now :P
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook