Use MATLAB or FreeMat

Problem (1), (2), and (3), use Bisection method, Secant iteration method. Answer the following by organize your result in a table on MATLAB or FreeMat. (i) How many iterations for each problems are needed to get five decimals correctly? (ii) What intervals for each bisection method were to use to obtain the result? What initial guess for secant method were to use to obtain the result?

1. Find all zeros of the following Legendre Polynomials (five decimals correctly).

(a) P2(x) = 0.5(3x2 1) (b) P3(x) = 0.5(5x3 3x)

(c) P4(x) = 35x4 30x2 + 3 8

2. Find the first five positive zeros of f (x) = x cos(x) + sin(x) (five decimals correctly). 3. Find all positive zeros of the function g(x) = 0.0001 + 1 (five decimals correctly)

1+x2