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Thread: Question about a Limit

  1. #1 Question about a Limit 
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    I got this Limit problem i cannot solve, i would really appreciate if someone can help me to figure it out, thanks!

    Lim (x/1-cos^2(x/2))
    x-> 0

    Thanks again!


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  3. #2  
    Forum Professor wallaby's Avatar
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    Since you cannot solve it i take that to mean that you have tried at least once? what approach did you use?


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  4. #3  
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    Yes indeed, i´ve tried not just once but many times, i tried using substitutions, identities, but non of them seems to work out.
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  5. #4  
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    Quote Originally Posted by Cideos View Post
    I got this Limit problem i cannot solve, i would really appreciate if someone can help me to figure it out, thanks!

    Lim (x/1-cos^2(x/2))
    x-> 0

    Thanks again!
    Comment 1: Should the expression be x/(1-cos^2(x/2)) ? As it stands it looks like x - cos^2(x/2).

    Assuming that I have corrected it properly, have you used Hospital's rule?
    Also you could simplify by 1 - cos^2(x/2) = sin^2(x/2).
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  6. #5  
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    Quote Originally Posted by mathman View Post
    Quote Originally Posted by Cideos View Post
    I got this Limit problem i cannot solve, i would really appreciate if someone can help me to figure it out, thanks!

    Lim (x/1-cos^2(x/2))
    x-> 0

    Thanks again!
    Comment 1: Should the expression be x/(1-cos^2(x/2)) ? As it stands it looks like x - cos^2(x/2).

    Assuming that I have corrected it properly, have you used Hospital's rule?
    Also you could simplify by 1 - cos^2(x/2) = sin^2(x/2).
    Yes, i didnt notice that mistake, and it is x/(1-cos^2(x/2)), thank you!.
    I know i can simplify it with using many identities, but i have tried many times and in many ways and still cant solve it.

    Also, one of the conditions my teacher gave me was to not use L'Hôpital's rule. I really would appreciate if you can help me!
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  7. #6  
    Forum Professor jrmonroe's Avatar
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    The x part seems trivial, so we're looking at the 1-cos²(x/2).

    Does 1-cos² remind you of anything?

    And the x/2 argument makes me think of half-angle formulas.

    Not that these two ideas must be resolved in the same step.

    Hopefully it should start coming together in your mind.
    Grief is the price we pay for love. (CM Parkes) Our postillion has been struck by lightning. (Unknown) War is always the choice of the chosen who will not have to fight. (Bono) The years tell much what the days never knew. (RW Emerson) Reality is not always probable, or likely. (JL Borges)
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  8. #7  
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    Quote Originally Posted by jrmonroe View Post
    The x part seems trivial, so we're looking at the 1-cos²(x/2).

    Does 1-cos² remind you of anything?

    And the x/2 argument makes me think of half-angle formulas.

    Not that these two ideas must be resolved in the same step.

    Hopefully it should start coming together in your mind.
    Thanks for the suggestion, but i´ve tried, as i wrote, with pitagoric identities, sum of angles, etc, and has not been of help.
    But thanks for the interest.
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  9. #8  
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    Okay, then do the worst thing possible ... throw it into a spreadsheet, and see how it behaves. It approaches infinity, of course, but it does so in a particular way. This gives the answer, but is probably not the "work" your teacher wants to see.
    Grief is the price we pay for love. (CM Parkes) Our postillion has been struck by lightning. (Unknown) War is always the choice of the chosen who will not have to fight. (Bono) The years tell much what the days never knew. (RW Emerson) Reality is not always probable, or likely. (JL Borges)
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