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Math Help - The Sandwich Theorem

  1. #1
    Member >_<SHY_GUY>_<'s Avatar
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    Question The Sandwich Theorem

    Used To Be Able To Find The Limit And Confirm It. I Really Don't Know How To Use The Sandwich Theorem.

    I just don't understand how and when to use it, for example:

    lim x-> infinity (1-cosx) / x^2

    in the book, it gives and example ofsinx / x which i get up to some point, and then i lose myself :/

    Thank you in advance
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  2. #2
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    Quote Originally Posted by >_<SHY_GUY>_< View Post
    Used To Be Able To Find The Limit And Confirm It. I Really Don't Know How To Use The Sandwich Theorem.

    I just don't understand how and when to use it, for example:

    lim x-> infinity (1-cosx) / x^2

    in the book, it gives and example ofsinx / x which i get up to some point, and then i lose myself :/

    Thank you in advance
    The Largest possible value of cos(x) is 1 so the smallest possible value of 1- cos x is 0. The smallest possible value of cos(x) is -1 so the largest possible value of 1- cos x is 2: [tex]0\le 1- cos x\le 2[/itex]. That means (dividing through be x^2 that 0\le \frac{1- cos x}{x^2}\le \frac{2}{x^2} because both 0 and \frac{2}{x^2} go to 0, and \frac{1- cos}{x^2} is "sandwiched between them", it must also go to 0.
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  3. #3
    Member >_<SHY_GUY>_<'s Avatar
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    Quote Originally Posted by HallsofIvy View Post
    The Largest possible value of cos(x) is 1 so the smallest possible value of 1- cos x is 0. The smallest possible value of cos(x) is -1 so the largest possible value of 1- cos x is 2: [tex]0\le 1- cos x\le 2[/itex]. That means (dividing through be x^2 that 0\le \frac{1- cos x}{x^2}\le \frac{2}{x^2} because both 0 and \frac{2}{x^2} go to 0, and \frac{1- cos}{x^2} is "sandwiched between them", it must also go to 0.
    following that equation, how can you tell that the limit is 0? [im sorry if you had alredy answered that, it confusing somewhat].
    and how can you use the sandwich theorem for any other equation? does it follow any steps?
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  4. #4
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    Hi

    i had the same problem, until i watch this on you tube.

    The person explains clearly what the sandwhich Theorem (or the Squeeze Theorem which the person calls it) is.




    and shows a good example of the Proof: lim (sin x)/x = 1

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