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March 20th, 2012, 09:30 PM  #1 
Member Joined: Feb 2012 Posts: 44 Thanks: 0  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 
March 20th, 2012, 10:06 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  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. 
March 20th, 2012, 10:17 PM  #3 
Member Joined: Feb 2012 Posts: 44 Thanks: 0  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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