Course Name : numerical methods for scientists & engineers

For a given function f (x), the divided-differences table is given by: XO = 0 f [xo] = a X1 = 1 f [x]] = b f[xo,x] =-1 X2 = 2 f [x2] = 20 f [x1, X2] = c f[xox, x2] = d X3 = 3 f [x3] =35 f [x2, X3] = 15 f [x1, x2,X3] = 7 f [xo, X1, X2, X3] = 2 The values of a is: O 20 O 19 O 17 O 22 * The approximation of the root x* of the function f (x) = -x + sin x - 1 accurate to within 10 3 using Secant's method starting with x. = -1.8 and x1 = -2 : O Needs 1 iterations O Needs 4 iterations O Needs 2 iterations O Needs 3 iterations