Solve by fixed point iteration and answer related questions where indicated Show details Let f(x) x 3 2x 2 3x 4 0 Write this as x g(x), for g choosing (1) (x 3 f) 1 3 , (2) (x 2 1 2f) 1 2 , (3) x 1 3f, (4) (x 3 f) x 2 , (5) (2x 2 f) (2x), and (6) x f f ' and in each case x 0 1 5 Find out about conv...

Roots r 1 156155 6Svalue r 2 1 exact r 3 256155 6Svalue 1r 1 12 steps ...

Solve by fixed-point iteration and answer related questions where indicated. Show details. Let f(x) = x 3

Question:

Solve by fixed-point iteration and answer related questions where indicated. Show details.

Let f(x) = x³ + 2x² - 3x - 4 = 0. Write this as x = g(x), for g choosing (1) (x³ - f)^1/3, (2) (x² - 1/2f)^1/2, (3) x + 1/3f, (4) (x³ - f)/x², (5) (2x² -f)/(2x), and (6) x - f/f' and in each case x₀ = 1.5. Find out about convergence and divergence and the number of steps to reach 6S values of a root.