(10 points) Implement into code: Let a be a fixed positive number, let 1 f(1) a, I and consider finding the solution of f(1) = 0) with Newton's method. This procedure is used in some computers to avoid hard-coded division by a. (a) Implement the Newton iteration. Notice that it converges if 0 1/a? (b) Use Newton iterations to approximate 1/e: observe how the error decreases over iterations and report the observed asymptotic constant. (10 points) Implement into code: Let a be a fixed positive number, let 1 f(1) a, I and consider finding the solution of f(1) = 0) with Newton's method. This procedure is used in some computers to avoid hard-coded division by a. (a) Implement the Newton iteration. Notice that it converges if 0 1/a? (b) Use Newton iterations to approximate 1/e: observe how the error decreases over iterations and report the observed asymptotic constant