(a) To approximate an irrational number of the form √, we can find a polynomial function : R → R with integer coefficients so that (√) = 0 and apply Newton's Method. Find such a and write out the resulting Newton iteration scheme. (b) Sketch the corresponding cobweb diagram and comment on the eventual fate of initial conditions. (c) Use the stability criterion from Problem 1 to show that the steady-states are stable. (In fact, they are what we call 'superstable.' This result is generalizable and explains why the convergence of Newton's method is typically so fast!)