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Determining a trigonometric limit

  1. May 10, 2017 #1
    1. The problem statement, all variables and given/known data
    Calculate the following limit:

    png.png

    2. Relevant equations


    3. The attempt at a solution
    I don't know how to proceed with this. I've tried to multiply by the conjugate, and to simplify the expression [itex](x+\pi)[/itex] to [itex]u[/itex], but I wasn't very sucessful. To what kind of algebric device I could resort to? Or is there other way to deduce the limit?
     
  2. jcsd
  3. May 10, 2017 #2

    LCKurtz

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    The problem as written is continuous at ##x=0##, so just plug it in. Or if both terms in the denominator are supposed to be cube roots, try L'Hospital's rule.
     
  4. May 10, 2017 #3

    Ray Vickson

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    I assume you meant to write ##\sqrt[3]{x+\pi}## instead of ##3 \sqrt{x+\pi}## in the denominator. If you do not want to (or are unable to) use calculus, use instead the algebraic identity ##a^3-b^3 = (a-b)(a^2+a b + b^2)## for appropriate ##a## and ##b##.
     
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