Answers

f(x) = cos(x) - x :

Inspecting the graph of f(x) we see there is one solution near x = 1.

Starting with an x₀ near 1, yields an approximation near  0.73985.

f(x) = x⁵ - 7x² + 2: 

Inspecting the graph of f(x) we see there are three solutions, one near x = -1, one near x = 1, and one near x = 3.

Starting at x₀  = -1, yields an approximation near  -0.52896.

Starting at x₀  = 1, yields an approximation near  0..54066.

Starting at x₀  = 3, yields an approximation near  1.85867.

f(x) = x²cos(x) - x:

Inspecting the graph of f(x) we see there are infinitely many solutions.

Starting at x₀  = 0, yields an approximation near 0.

Starting at x₀  = 5, yields an approximation near  4.91719.

Starting at x₀  = 8, yields an approximation near  7.72415.

Copyright c 1996 by Steve Hetzler and Bob Tardiff Department of Mathematics and Computer Science, Salisbury State University, Salisbury, MD 21801.