Please answer the following questions in complete sentences in a typed manuscript and submit the solution on blackboard by on April 18th at noon.
Please identify anyone, whether or not they are in the class, with whom you discussed your homework. This problem is worth 1 point, but on a multiplicative scale.
Make sure you have included your source-code and prepared your solution according to the most recent Piazza note on homework submissions.
Consider the equation
Show graphically, as simply as possible, that in the interval there is exactly one root .
Does Newton's method converge to a root if the initial approximation is taken to be ? Justify your answer.
Consider Newton's method for computing . Let .
Show that
Use (1) to show that Discuss the significance of this result with regard to the overall behavior of Newton's iteration.
Express the Newton iteration for solving these systems of equations and show (analytically or experimentally) what happens if you start from .
,
,
Can either of the two systems above be solved via the fixed-point method? Two variations on the fixed point method to consider are:
Do either of those modifications help? (This problem requires you to implement and investigate.)