1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(æ) = 0. You should give your values of f to four significant figures. (b) With a = 1 and b = 2,...

Extracted text: 1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(æ) = 0. You should give your values of f to four significant figures. (b) With a = 1 and b = 2, the first two iterations of the bisection method for the function given in part (a) are shown in the following table. Do two more iterations to find the missing values in the table which are denoted by ???. bn f(æn) 1.1463 n An an 1 1 2 1.5 1 1.5 1.25 -0.3266 ??? ??? 3 ??? ??? ??? 4 ??? ??? ??? (c) For the function f of part (a), write down the corresponding Newton-Raphson method. Then take xo = 1 and do two iterations of this method. You should give your values of x1 and x2 to six significant figures.