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Trig Limit Question

  1. Oct 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the limit as x approaches ∏/8, (cos(2x)-√(2))/(x-∏/8)


    2. Relevant equations

    cos(2x)+cos(2a)


    3. The attempt at a solution

    I tried to multiply the conjugate of the terms but ended up stuck there, don't know how to go on. Please help.
     
  2. jcsd
  3. Oct 13, 2011 #2

    Mark44

    Staff: Mentor

    This isn't an equation, and I don't see how it's relevant to anything.
    As x approaches [itex]\pi[/itex]/8, what does the numerator approach? What does the denominator approach?
     
  4. Oct 13, 2011 #3
    You end up with -(1/sqrt2)/0 limit. the equation is an identity that is supposed to help when solving the question.

    I also tried expanding the relevant equation and ended up with, cos(2x)+cos(2a)=-2sin(x+a)sin(x-a)
     
  5. Oct 13, 2011 #4

    Mark44

    Staff: Mentor

    cos(2x)+cos(2a) is NOT an equation, so it can't possibly be an identity.
    But that's not a number. I agree that the numerator approaches -1/sqrt(2), which is the same as -sqrt(2)/2. And I agree that the denominator approaches 0.

    So this problem is similar to these limits:

    [tex]\lim_{x \to 0}\frac{1}{x}[/tex]
    [tex]\lim_{x \to 0}\frac{1}{x^2}[/tex]

    How would you characterize these two? (One of them has a direct bearing on your limit.)
     
  6. Oct 13, 2011 #5
    I am not exactly sure about that.

     
  7. Oct 13, 2011 #6

    Mark44

    Staff: Mentor

    What is it that you're not exactly sure about? If you think that cos(2x)+cos(2a) is an identity, I am absolutely certain that you are wrong.

    Are you unsure that your limit is related to one of the ones I gave, you can start by answering my question.
     
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