- #1

lunia

- 5

- 0

**Task**

Use the Bisection, Newton, and Secant methods to solve (to at least 8

signicant figures) the equation

sin(x) = 0.98 cos(2x2)over the interval [0, 2.5], in radiant units. For the Newton method, try with

several different initial guesses including x0 = 1. With the Secant method,

use the same initial values as for the Bisection, as well as other appropriate

values. Comment on the results by comparing the effectiveness of

each method for this problem. In particular, compare the number of iterations

required by each method to find the solution to a specied accuracy

(at least|f(xroot)| ≤ 10−6

), and see if the behavior you observe tallies with

theoretical predictions where they have been given, in particular the order of

convergence. Provide a careful explanation on your observations.

**Hint**

Draw a graph of the equation to understand the behaviors of the equation,

such as the number of solutions and the locations of the roots.

p/s: basicly i don't even know what this question want exactly, i do try my best to understand it but i cant. I am sorry