Documents and calculate are forbidden Solve problems 1 2 3 a

Documents and calculate are forbidden. Solve problems 1, 2, 3 and (4A or 4B). Written on a complete pseudo-code implementing the following method to determine the solution x to f(x) = alpha. Try as much as possible to use matlab/s syntax and comment your code. Setting epsilon > 0 small enough, and for x0 R, one define the sequence (xn)n by x n+1 = xn - epsilon(f(xn) - alpha) / f(xn + epsilon) - f(xn). Assume that alpha n rightarrow 0, x n = (alpha n) and y n = (alpha n). Prove that xn yn = 0(alpha n). Prove that if xn = 0(alpha n) and yn = 0(alpha n),then xn + yn = 0(alpha n). Determine the Lagrange polynomial P at (-1,7),(0,5), (1,5).

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