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Homework Help: Continuity Proof

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data

    f(x) = x^3 [cos(pi/x^2) + sin(pi/x^2)] for x≠0

    2. Relevant equations

    3. The attempt at a solution

    I really am stuck.

    I've tried squeeze theorem on [cos(pi/x^2) + sin(pi/x^2)], but I can't compute the range.

    So, I tried doing it individually, squeezing -1 ≤ cos(pi/x^2) ≤ 1, but that doesn't work.

    Any hints please?
  2. jcsd
  3. Oct 15, 2011 #2


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    cos(θ)+sin(θ) = (√2)sin(θ + π/4)
  4. Oct 15, 2011 #3


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    What's the question exactly? You want to prove that that function is continuous?
  5. Oct 16, 2011 #4


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    The given function is obviously continuous for [itex]x\ne 0[/itex] because it is a composition of continuous functions. It obviously not continuous for x= 0 because it is not defined at x= 0.

    Because I suspect the problem was not supposed to be that "obvious", please check again and tell us what the problem really is!
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