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March 20th, 2012, 09:30 PM   #1
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A calculus question with limits and differentials

Based on these four functions:

1. f(x) = 1/(sqrt)x
2. f(x) = e^-x
3. f(x) = 1/(x^2)
4. f(x) = 1/lnx

-All of these functions are decay functions, with limit of 0 as x -> infinity. Which decays the fastest? What are the values of each function (approximatley) at x = 100?
-Which of the functions satisfies this differential equation? x^2f^(2 prime) + xf^(prime) - (f/4) = 0
-Which of the functions satisfies this differential equation? x^2f^(2 prime) + xf^(prime) + (f/3) = 0

I haven't worked alot with the f prime stuff so i'm pretty confused on how to approach these. Any help would be awesome
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March 20th, 2012, 10:06 PM   #2
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Re: A calculus question with limits and differentials

One way to determine which decays the fastest is to look at whose denominator grows the fastest. You should verify this is number 2.

Use your calculator to obtain the values of the functions for x = 100.

Take the first and second derivatives of each function and substitute into the given differential equations to see which one satisfies them. Are you sure the second differential equation is correct? None of the given functions satisfies it.
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March 20th, 2012, 10:17 PM   #3
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Re: A calculus question with limits and differentials

Yes, they are both similar. I should have wrote them something like this:

x^2f" + xf' + (f/3) = 0

Thanks for the help.
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