roots_and_optimization

homework 3

i. Compare the number of iterations that each function needed to reach an accuracy of 0.00001%. Include a table in your README.md with:

| solver | initial guess(es) | ea | number of iterations|
| --- | --- | ---  | --- |
|falsepos   | 1,5  | 3.3027      | 1.1363 e-0.7 |
|incsearch  | 1,5  | 66.2618     | 5.0248 e-0.7 |
|newtraph   | 1    | 3.4172 e-07 | 802          |
|mod_secant | 1    | 0.0014      | 3            |

convergence of the four different methods falsepos, bisect, newtraph and mod_secant being used to solve for the angle of the projecitle function with an initial velocity of 15 m/s. the approximated error is being plotted against the number of iterations

divergence of Newton-Raphson method

iteration	x_i	approx error
0	2	n/a
1	2	12.5000
2	2	9.5703
3	2	7.8262
4	2	6.6491
5	2	5.7943

| - | -- | --- | | 0 | 0.2 | n/a | | 1 | 0.2 | 1.2500 e+0.3 | | 2 | 0.2 | 1.6531 e+0.5 | | 3 | 0.2 | 4.5122 e+11 | | 4 | 0.2 | 4.5122 e+11 | | 5 | 0.2 | 4.5122 e+11 |

Homework #4