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.
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