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4. Let f(x)=-3x4 – x² + 2x +11. (a) Show that the equation f(x) = 0 has a unique root a in (-2, -1]. (b) Find the Newton
Posted: Thu May 12, 2022 10:24 am
by answerhappygod
- 4 Let F X 3x4 X 2x 11 A Show That The Equation F X 0 Has A Unique Root A In 2 1 B Find The Newton 1 (49.95 KiB) Viewed 21 times
4. Let f(x)=-3x4 – x² + 2x +11. (a) Show that the equation f(x) = 0 has a unique root a in (-2, -1]. (b) Find the Newton's iterative formula for solving the equation f(x) = 0. g(x,-1) [Give the formula in the form x where g(x,-1) and h(x,-1) are polynomial functions.] h(x,-1) = (c) Show that the sequence obtained by the iterative formula in (b) will converge to a for any initial guess x, in (-2,-1]. (d) Hence, with x, =-1.5, estimate the value of a correct to 4 decimal places. =- (25 marks)