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Limits of Trigonometric Functions. !

  1. May 2, 2010 #1
    Limits of Trigonometric Functions. URGENT!

    1. The problem statement, all variables and given/known data
    Evaluate stackrel{lim}{x [tex]\rightarrow[/tex]0}[/tex] [sin(\frac{2e}{x3}) \bullet (arctanx)]

    2. Relevant equations
    All I know is that the equation stackrel{lim}{x [tex]\rightarrow[/tex]0}[/tex] [tex]\frac{sin x}{x}[/tex] = 1 might be helpful, but I'm not sure how to apply it to this particular problem.

    3. The attempt at a solution
    I talked to a friend of mine who's in Calc III, and she said that the whole limit would be equal to 0 since arctan(0) = 0, and sin[tex]\frac{2e}{x3}[/tex] is undefined, and the zero beats out the undefined value. This might be right, but how would I show that mathematically?

    All help is greatly appreciated as I'm kind of in a crunch here :)
  2. jcsd
  3. May 3, 2010 #2


    Staff: Mentor

    Re: Limits of Trigonometric Functions. URGENT!

    Here's your corrected limit expression.

    Evaluate [tex]lim_{x \rightarrow 0} sin(\frac{2e}{x^3}) arctanx[/tex]

    Your friend is leading you astray. It's not necessarily true that an expression tending to zero "beats out" an undefined value. What is true is that -1 <= sin(u) <= 1 for all real values of u.
  4. May 3, 2010 #3
    Re: Limits of Trigonometric Functions. URGENT!

    Thanks for correcting my formatting. I was in a rush, and I accidentally hit the "submit post" button before previewing it.

    Thanks for the input!!
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