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Math Help - Use Riemann sums and a limit to compute the exact area under the curve.

  1. #16
    MHF Contributor MarkFL's Avatar
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    Re: Use Riemann sums and a limit to compute the exact area under the curve.

    Once I have the form:

    A_n=\frac{(n+1)(11n+1)}{6n^2}

    I know it is of the form:

    A_n=\frac{11n^2+\cdots}{6n^2}

    and since the degree is the same in the numerator and denominator, I know the limit as n\to\infty is simply the ratio of the leading coefficients, so we must have:

    \lim_{n\to\infty}A_n=\frac{11}{6}

    There is nothing wrong with your approach either, I just find it simpler to think of the technique we are taught in precalculus to find horizontal asymptotes.
    Thanks from JDS
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  2. #17
    JDS
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    Re: Use Riemann sums and a limit to compute the exact area under the curve.

    Okay, I took your advice and reworked the problem and voila, now I get the same answer either way! I posted my work in the attached pic file, just for your perusing pleasure

    Thanks for all your help, you ROCK!
    Attached Thumbnails Attached Thumbnails Use Riemann sums and a limit to compute the exact area under the curve.-new-method-reworked.jpg  
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  3. #18
    JDS
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    Re: Use Riemann sums and a limit to compute the exact area under the curve.

    Quote Originally Posted by MarkFL2 View Post
    Once I have the form:

    A_n=\frac{(n+1)(11n+1)}{6n^2}

    I know it is of the form:

    A_n=\frac{11n^2+\cdots}{6n^2}

    and since the degree is the same in the numerator and denominator, I know the limit as n\to\infty is simply the ratio of the leading coefficients, so we must have:

    \lim_{n\to\infty}A_n=\frac{11}{6}

    There is nothing wrong with your approach either, I just find it simpler to think of the technique we are taught in precalculus to find horizontal asymptotes.
    Very good advice. It has been eons and eons since I took Algebra, let alone pre-calculus, which explains why I am not very efficient at these yet. I suppose "Hind sight is 20/20" and I should not have dove straight into calculus without some basic refreshers.

    Once again, you have saved me much anguish! I truly thank you!!
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  4. #19
    MHF Contributor MarkFL's Avatar
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    Re: Use Riemann sums and a limit to compute the exact area under the curve.

    Your revised work looks good! Glad to be of assistance.
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