Numerical Analysis

Problem 1. [50 Relative Points). Find 12 = '3' for the rnction f(x) = (x2 + B)sln(x) using Newton's Method for approximation of the root on the interval [2, 3.7]. Round up your results to two digits after the decimal point. Show the graph of the function on the interval [2, 5]. Consider 2. 3.? and 5 as radians for the trigonometric functions. Note: You have to prove the three conditions are satised in order to apply the method. Problem 1. {52 Relative Points} Given the Vasko Popov method with the equation @(x) = x - 13:1.) on the interval [3, b]EDf. Assume that: 1) f"(x) , for) and 11x) continuous on lath]; 2) u) > 0. f(a)f"(a) 2-: u; 3) f\"(x) and f'(x) do not change sign on [a., h]; 4] siynU' ((1)) at sign((fb)). Prove that Iqr'(x)| c: 1 'E