University of Florida/Egm4313/s12.team11.gooding/R4
Problem 4.4 Parts 1,2
editPart 1
editProblem Statement
editFind n sufficiently high so that do not differ from the numerical solution by more than at
Solution
editUsing 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
editProblem Statement
editDevelop in Taylor series about for and plot these truncated series vs. the exact function.
What is now the domain of convergence by observation?
Solution
editA 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)