Question

5. For each of the following functions, and the corresponding initial interval, tell whether Bisection method can be applied to find a root in the interval, and if so, how many iterations are required to achieve the associated accuracy. Recall 10-G1 (b-a). (a) f(x) = sin(x), [-1, 1], E = 2-16 (b) f(x) = sn'(x), [-1, 1], € = 2-16 (c) f(z) = cos(x), [-1, 1], ε = 2-16

Answer 1

Given that (a) f (x) = Sin x [- 1, 1], E = 2^- 16 Now, f (- 1) = Sin (- 1) = -0 017452 f (1) = sin (1) = 0 017452 f (- 1) f (1) < 0 then, bisection method can be applied here by using the formula the number of iterations is n greater than or equal to log (b - a) - log E/log2 if b = 1, a = -1 E = 2^- 16 n greater than or equal to log2 - log (2^- 16)/log2 n greater than or equal to log2/log2 - log (2^- 16)/log2 \r\n n greater than or equal to 1 + 16 n greater than or equal to 17 (b) f (x) = sin^2 x, [- 1, 1] f (- 1) = sin^2 (- 1) f (- 1) = 0 01742 and f (1) = sin^2 (1) = 0 01742 Now bijection method cannot be applied here