Basins of attraction Suppose f has a real root r and

Chapter 4, Problem 49

(choose chapter or problem)

Basins of attraction Suppose f has a real root r and Newtons method is used to approximate r with an initial approximation x0. The basin of attraction of r is the set of initial approximations that produce a sequence that converges to r. Points near r are often in the basin of attraction of rbut not always. Sometimes an initial approximation x0 may produce a sequence that doesnt converge, and sometimes an initial approximation x0 may produce a sequence that converges to a distant root. Let f 1x2 = 1x + 221x + 121x - 32, which has roots x = -2, -1, and 3. Use Newtons method with initial approximations on the interval 3-4, 44 to determine (approximately) the basin of each root.

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back