Sherrie F.

For each initial approximation, determine graphically what happens if Newton's method is used for the function whose graph is shown.
(a) $ x_1 = 0 $ (b) $ x_1 = 1 $ (c) $ x_1 = 3 $
(d) $ x_1 = 4 $ (e) $ x_1 = 5 $

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ x^5 - 3x^4 + x^3 - x^2 + 6 = 0 $

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ \dfrac{x}{x^2 + 1} = \sqrt{1 - x} $

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ \cos (x^2 - x) = x^4 $

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ 4e^{-x^2} \sin x = x^2 - x + 1 $

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ \ln (x^2 + 2) = \dfrac{3x}{\sqrt{x^2 + 1}} $