1. Consider the linear discrete dynamical system xn+1 = f(xn),1 , n = 0, 1, 2, ... with initial value x0 = 0, where the real-valued function f is defined below. In each case, determine the explicit formula for xn, find all the equilibrium points and classify them as stable or unstable, and draw the cobweb diagram indicating the stability or otherwise of each equilibrium point. (a) f(x)=2x+1, (b) f(x) = x+1. 2. Consider the discrete dynamical system xn+1 = = x, n = 0, 1, 2, ... (1) where the initial value xo is a given real number. (a) Determine the explicit formula for xn. (b) Determine when lim xn exists. Express your answer in terms of xo. nx (c) Find all the equilibrium points and classify them as stable or unsta- ble. (d) Let a be a fixed positive real number, and consider the dynamical system xn+1 = ax, n = 0, 1, 2, ... where the initial value xo is a given real number. i. Let yn=axn, n=0, 1, 2, . . . Find the discrete dynamical system satisfied by the values yn and determine the explicit formula for Yn. (Use the part (a) above). ii. Determine the explicit formula for xn in part (i).