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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: 521 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. Tags calculus, differentials, limits, question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post philip Calculus 1 September 17th, 2013 07:31 AM ChanThar Calculus 2 September 9th, 2013 04:08 PM The Crisp Calculus 12 November 4th, 2012 12:03 PM studentx Applied Math 2 November 19th, 2011 12:54 AM madden Calculus 6 June 9th, 2010 04:53 PM

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