OMG Need Urgent Help with this question. I've been trying so hard but don't know where to start. Thanks!!

1. Consider the implicit Euler approximation 1% = yin1 + hf(tkayk) of the solution, 3;, to the ODE y' = f (t, y), y(t.;.) = yo. Suppose that f has continuous derivatives and that there is a constant M so that |f(t, y)| S M for all points (t,y). (a) Let R be the rectangle consisting of points (t, y) with 0 S t to 5 a and |y yo| S b for some positive constants a and b. Show that if tk to S or, where a = min {(1, %}, then (tk, yk) is contained in R. (b) Assume that tk to S a. Show that if E3: = |yk y(tk)| then Etcl + ED