University of Florida/Egm4313/s12.team11.gooding/R4

Problem 4.4 Parts 1,2

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Part 1

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Problem Statement

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Find n sufficiently high so that   do not differ from the numerical solution by more than   at  

Solution

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Using a program in MATLAB that iteratively added terms onto the taylor series of  , terms were added until the error between the exact answer and the series was less than  .

 

It was found after trial and error that   for the error to be of a magnitude of  . This error found was 9.7422e-005

Similarly, for  .

 

It was found after trial and error that   for the error to be of a magnitude of  . This error found was 9.3967e-005

Part 2

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Problem Statement

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Develop   in Taylor series about   for   and plot these truncated series vs. the exact function.
What is now the domain of convergence by observation?

Solution

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A MATLAB program was created, which calculated the Taylor series of each n value, along with the exact function, then plotted these together to show the comparison of all the series.
Below is the Taylor series for   expanded at  .
 

 
 
It can be seen by observation that the domain of convergence has shifted to the right one unit.

--egm4313.s12.team11.gooding (talk) 03:48, 14 March 2012 (UTC)