Suppose h, a, h,a, and bb are positive real numbers, and t_0, y_0t 0 ,y 0 are real numbers, and that f(t, y)f(t, y) is a function of tt and yy. Let t_n, ynt n ,y n satisfy the recursions t{n+1}=tn+h, \text{ and } \ y{n+1}= y_n+h f(t_n, y_n).t n+1 =t n +h, and y n+1 =y n +hf(t n ,y n ). Let RR be the rectangle in the tyty-plane given by: t_0\leq t\leq t_0+ at 0 ≤t≤t 0 +a, y_0- b\leq y\leq y_0+ by 0 −b≤y≤y 0 +b, and assume that |f(t, y)|\leq M∣f(t, y)∣≤M for all (t, y)(t, y) in RR. Finally, let \alpha = \min(a, b/ M)α=min(a, b/M). a) Prove that |y_j-y_0| \leq jhM∣y j −y 0 ∣≤jhM, as long as jh \leq \alphajh≤α. b) Conclude from (a) that the points (t_j, y_j)(t j ,y j ) all lie in RR as long as j \leq \alpha/h. j≤α/h