README.md

# Homework #3

#Question 1 Results

Part (i)

|   solver  | initial guess(es)      |    ea     | number of iterations|
| --- | --- | --- | --- |
|falsepos   |         1, 50          | 2.16e-06  |         10          |
|bisect     |         1, 50          | 3.94e-07  |          6          |
|newtraph   |         1, 50          | 9.92e-06  |         24          |
|mod_secant |         1, 50          | 7.63e-06  |        624          |

Part(iii)

  The file used to create the plots is "HW3_Script this file contains a series of for loops that take data from the root functions and places them into a "Table" from here it organizes the data and titles it. The convergence plot uses the information from the "Table" to plot the information on a a graph that is setup by calling the "setdefaults" function.

Part(ii)

check "convergence.png" graph

#Question 2 Results

Divergent

|   Iteration  | x_i   |Approx Error|
| --- | --- | --- |
|1             |  2    | 12.5       |
|2             |  2    |9.5703      |   
|3             |  2    |7.8262      |
|4             |  2    | 6.6491     | 
|5             |  2    | 5.7943     | 

Convergent

|   Iteration  | x_i   |Approx Error|
| --- | --- | --- |
|1             |  0.2  | 1250       |
|2             |  0.2  | 1.6531e05  |   
|3             |  0.2  |4.5122e11   |
|4             |  0.2  |4.5122e11   | 
|5             |  0.2  | 4.5122e11  |