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Evaluate each of the following limits. Show all reasoning.

  1. Feb 28, 2009 #1
    lim (2 tan^2 x)/x^2
    x->0

    I am just uncertain about how to do this question. Do I find a derivative or something else? Just need some guidance.

    Thanx.
     
  2. jcsd
  3. Feb 28, 2009 #2

    HallsofIvy

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    If it were me, I would rewrite tan x as sin x/cos x and try to break the expression into parts.
     
  4. Feb 28, 2009 #3
    Remind me please, do you rewrite tan as sin/cos before taking derivative or after? I think it is before, but not 100% sure. Thanks
     
  5. Feb 28, 2009 #4

    Dick

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    Halls is guessing you know the limit x->0 of sin(x)/x. If so just substitute it. Otherwise, use l'Hopital.
     
  6. Feb 28, 2009 #5

    HallsofIvy

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    Why in the world would you take any derivative?
     
  7. Mar 3, 2009 #6
    Ooooh.... I have thought of a completely different thing here. I understand it now.

    thanks guys!
     
  8. Mar 3, 2009 #7
    just wanted to confirm with you guys (finding this topic a little difficult)

    by converting tan^2x i get

    lim 2sin^2x
    x->0 cos^2x(x^2)

    limit x->0 of sin^2x/x^2 gives 1 correct? then im simply left with 2/cos^2x which gives me final answer 2. Am I correct? Thanks for help/comments.
     
  9. Mar 3, 2009 #8

    Dick

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    Yes, that's it.
     
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