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December 27th, 2016, 12:41 AM  #1 
Newbie Joined: Dec 2016 From: turkey Posts: 1 Thanks: 0  Explaining the curious phenomenon that occurs Could you please help me on explaining the curious phenomenon that occurs for this question ? 
December 27th, 2016, 03:28 PM  #2 
Member Joined: Dec 2016 From: USA Posts: 46 Thanks: 11 
If done in floating point, you will quickly lose accuracy, to the point where the output is not only wrong, but blatantly wrong. I'm pretty sure that's the "curious phenomenon" you were advised about. There's nothing mathematically curious about the true values of $x_n$  they simply approach zero, slowly and boringly. What programming language are you planning to use? What data type will you use for the values of $x_n$? 
December 27th, 2016, 04:04 PM  #3 
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus 
This simple algorithm can be programmed on a graphing calculator easily. Using a CAS on the computer, however, it can be done with much greater precision.

December 27th, 2016, 07:41 PM  #4 
Member Joined: Aug 2016 From: Used to be Earth Posts: 64 Thanks: 14 
@Compendium Where can I find a proof of your profile picture? Thanks 
December 27th, 2016, 07:50 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,553 Thanks: 1403  
December 27th, 2016, 08:19 PM  #6 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out.  
December 28th, 2016, 02:50 AM  #7  
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus  Quote:
$\displaystyle 2\pi\int_{0}^{\infty}xe^{x^2}dx\,=\,\int_{\infty}^{\infty}\int_{\infty}^{\infty}e^{(x^2+y^2)}dx\,dy$. The left hand side should be easy to integrate. On the right hand side, the double integral is separable. Then the solution should become obvious. Last edited by Compendium; December 28th, 2016 at 03:19 AM.  
December 28th, 2016, 02:26 PM  #8  
Member Joined: Aug 2016 From: Used to be Earth Posts: 64 Thanks: 14  Quote:
 

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