x* – x – 1 = 0 i) Explain Secant algorithm. ii) Find positive root of the equation with error is less than 10-6 by Secant method for initial interval [0,2] in MATLAB (or any other computation tool.) iii) Obtain the table which contains n, xn, f (xn), | Xn – xn-1| values for each iteration step.

From course, Number Theory

The proof in the attached image is given for Bayes theorem, however I am quite a bit confused so if able please explain the proof in more detail step by step, thank you in advance.

92 (a) Determine the roots of fix)=-13-20x+ 19x-3x graphically. In addition, determine the first root of the function with (b) bisection. and (c) false position. For (b) and (c) use initial guesses of xy -1 1 and x 0. and a stopping criterion of 1%