Σ n+1 (n+2)! n=0

(b) For the function f from part (a), could the Bisection method be used to find a root in the interval [10, 10]? Say exactly why or why not. If it can be used, give two starting values that you could use which would guarantee that the Bisection method would converge to a root of f in [-10, 10]. (c) Let L be 1 Come up with a function which has root at x = L and for which the Bisection method could be successfully used to find L using x= 0 and x = L+2 as starting values. Next, calculate how many iterations of the Bisection method with starting values 0 and L+2 would be required to guarantee that the root L of f is approximated with an absolute error of 0.0001 or less (but also assuming you do not know that L is the root).

Verify that x = 1/a is a fixed point of the function g(x) x(2 ax). Determine the order of convergence and the asymptotic error constant of the iteration sequence Pn = 9(Pn-1) toward x = = 1/a. MOT = -

5). Find the interval of convergence.∞ n = 0xnn7 + 8