Let d1 = [nag = f(a1),a3 = f[oq),...,an+1 = an), Where a is some number and f is a continuous function. If lim on = L1 show that f{L} = L. nl-oo Now, let a = 1. Find an example of a function f such that the corresponding sequence converges and such that x) = a: has exactl}r 1 solution. Find an example of a function f such that the corresponding sequence converges and such that f{$) = x has more than one solution. Find an example of a function f such that the corresponding sequence diverges and such that st) = a: has no solution. Find an example of a function f such that the corresponding sequence diverges and such that x) = :1: has a solution