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Math Help - limit problem :(

  1. #1
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    Joined
    May 2009
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    limit problem :(

    hey everyone, i am new here and i need help as i have final today.
    I have no problem with dealing with limits, but i am having troubles with this one.

    lim sin(x^2) / [ ( e^x ) - x - 1 ]
    x-->0

    first, I know that this problem should be solved using l'hopital's rule.

    as i did it using it, i got to lim [ - cos(x^2) . 2x . 2x . 2x ] / e^x
    x-->0
    so my answer would be zero.

    is this right? because my teacher said in class that the answer for this should be 2 and i wonder how she got 2.

    please anyone would help?
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by weskerq8 View Post
    hey everyone, i am new here and i need help as i have final today.
    I have no problem with dealing with limits, but i am having troubles with this one.

    lim sin(x^2) / [ ( e^x ) - x - 1 ]
    x-->0

    first, I know that this problem should be solved using l'hopital's rule.

    as i did it using it, i got to lim [ - cos(x^2) . 2x . 2x . 2x ] / e^x
    x-->0
    so my answer would be zero.

    is this right? because my teacher said in class that the answer for this should be 2 and i wonder how she got 2.

    please anyone would help?
    First Step

    Differentiate Numerator
    its = cos(x^2)* 2x

    Doing so with denominator
    its =e^x - 1
    _________________________________________________
    Second Step

    Differentiate Numerator again
    i

    \frac{d}{dx}(cos(x^2)*2x)= -sin(x^2)*2x * 2x + cos(x^2)*2 <br />
--Use chain Rule

    Doing so with denominator again
    its = e^x
    Now pt the limit.Answer = 2
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  3. #3
    Newbie
    Joined
    May 2009
    Posts
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    Thank you very much for the help
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