3. (Adapted from FNC 4.2.1 and 4.2.2.) In each case below, 9(8) = (x + %), r = 3. g(x) = 1 + 1 sin(x), r = . g(x) = x +1 tan(x/4), r = . . . (a) (by hand) Show that the given g(x) has a fixed point at the given r and that fixed point iteration can converge to it. (b) (computer) Apply fixed point iteration in MATLAB and use a log-linear graph (using semilogy) of the error to verify linear convergence. Then use numerical values of the error to determine an approximate value for the rate o (see Lecture 22). 3. (Adapted from FNC 4.2.1 and 4.2.2.) In each case below, 9(8) = (x + %), r = 3. g(x) = 1 + 1 sin(x), r = . g(x) = x +1 tan(x/4), r = . . . (a) (by hand) Show that the given g(x) has a fixed point at the given r and that fixed point iteration can converge to it. (b) (computer) Apply fixed point iteration in MATLAB and use a log-linear graph (using semilogy) of the error to verify linear convergence. Then use numerical values of the error to determine an approximate value for the rate o (see Lecture 22)