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Systematically avoiding arbitarily large exponents in calculations with small answers

  1. Dec 6, 2011 #1
    [tex]y=\frac{100}{100}\frac{\frac{(((100/100)^2-100*100)e^{x/(100*100)}+(100*100))e^{-x/(100*100)})-(100/100)^2e^{-x*100/100}}{100/100-100*100}}{1}[/tex]

    http://www.quickmath.com/msolver//graphs/2011-12-06/e5/61/e2/e561e26ac85a4b1da0176565a4827772-2.png?t=1323201139 [Broken]

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    704 #NUM!
     
    How do I avoid arbitrarily large exponents in calculations with such small answers? Is there a way of getting rid of them?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 6, 2011 #2

    mathman

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    Science Advisor
    Gold Member

    Re: Systematically avoiding arbitarily large exponents in calculations with small ans

    You need to clarify your expression. You have several terms (100/100 = 1) which are confusing. Other terms are 100*100 = 10000. Why the product?
     
  4. Dec 6, 2011 #3
    Re: Systematically avoiding arbitarily large exponents in calculations with small ans

    Modified:

     
    Last edited by a moderator: May 5, 2017
  5. Dec 7, 2011 #4

    mathman

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    Science Advisor
    Gold Member

    Re: Systematically avoiding arbitarily large exponents in calculations with small ans

    You could start by using the approximation eu = 1 + u + u2/2 for small u.
     
  6. Dec 7, 2011 #5

    Stephen Tashi

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    Science Advisor

    Re: Systematically avoiding arbitarily large exponents in calculations with small ans

    kmarinas86,

    The parentheses aren't balanced in your modified version.
     
  7. Dec 14, 2011 #6
    Re: Systematically avoiding arbitarily large exponents in calculations with small ans

    It appears that this was easier than I thought:

    [tex]y=\frac{100}{100}\frac{\frac{((((100/100)^2-100*100)e^{x/(100*100)}+(100*100))e^{-x/(100*100)})-(100/100)^2e^{-x*100/100}}{100/100-100*100}}{1}[/tex]

    [tex]y=\frac{100}{100}\frac{((((100/100)^2-100*100)e^{x/(100*100)}+(100*100))e^{-x/(100*100)})-(100/100)^2e^{-x*100/100}}{100/100-100*100}[/tex]

    [tex]y=\frac{(((1-10000)e^{x/10000}+10000)e^{-x/10000})-e^{-x}}{1-10000}[/tex]

    [tex]y=\frac{(((1-10000)e^{x/10000}e^{-x/10000})+10000e^{-x/10000}))-e^{-x}}{1-10000}[/tex]

    [tex]1=e^{x}e^{-x}[/tex]

    [tex]y=\frac{1-10000+10000e^{-x/10000}-e^{-x}}{1-10000}[/tex]

    I figured this out a few days ago, but I hadn't decided to post it until now.
     
    Last edited by a moderator: May 5, 2017
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