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Evaluating Limits with trig functions

  1. Jul 11, 2012 #1
    1. The problem statement, all variables and given/known data
    lim x-->0 sin(pi/x) sqrt(x^3+x^2)




    3. The attempt at a solution

    I was having trouble evaluating the above limit. Do I start by isolating x? For some reason, when it comes to trig functions such as this, I'm not sure how to simplify it. Also, what material would I have to review for me to understand how to break down such trig functions? I'm aware of fundamental, quotient and reciprocal identities of trig functions but am not sure how to use that knowledge to solve these type of problems.
     
  2. jcsd
  3. Jul 11, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    As x goes to 0, sin(pi/x) oscillates but stays between -1 and 1. That is,
    [tex]-\sqrt{x^3+ x^2}\le sin(\pi/x)\sqrt{x^3+ x^2}\le \sqrt{x^3+ x^2}[/tex]
     
  4. Jul 11, 2012 #3

    Zondrina

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    Homework Helper

    Use the fact that :

    |sin(x)| ≤ 1 [itex]\forall[/itex]x[itex]\ni[/itex]R

    As in FOR ALL x you happen to plug in to the sin function including whatever value gets spat out of pi/x.

    hint hint ;)
     
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