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

## Problem 4.4 Parts 1,2[edit | edit source]

### Part 1[edit | edit source]

#### Problem Statement[edit | edit source]

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

#### Solution[edit | edit source]

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[edit | edit source]

#### Problem Statement[edit | edit source]

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[edit | edit source]

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)