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Help with evaluating a limit

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data

    lim (1-tan x) / (sin x - cos x)

    2. Relevant equations

    3. The attempt at a solution

    Im not sure where to start with this one. Should I turn tan x into sinx/cos x and try to do cancel some of the equation out?
  2. jcsd
  3. Jan 26, 2009 #2


    Staff: Mentor

    That might work. Another approach is L'Hopital's Rule if you know it, since this expression has the indeterminate form 0/0.
  4. Jan 26, 2009 #3


    User Avatar
    Gold Member

    I just tried what you suggest and it came out okay.
  5. Jan 27, 2009 #4
    Well I did some work with the equation and got 2/sqrt 2

    This is how I got there,

    I made the 1 = cos x/cos x
    The tan x = sin x/cos x

    Then I brought the denomenator up which canceled out both sin x - cos x which left me with 1 / -cos x

    I plugged in the pi/4 which is sqrt 2/2 , which equals -2/sqrt2, which equals -sqrt2

    What do you guys think?
    Last edited: Jan 27, 2009
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