This exercise outlines the proof of the fact that the Picard iterates are defined. Show th...

This exercise outlines the proof of the fact that the Picard iterates are defined. Show that if (x, pn(x)) lies in the rectangle |x – x0| < a and |y – y0| < b, then . Use this to show that if h is the minimum of b/K and a, then the Picard iterates are defined for |x – x0| ≤ h.