- 4 Let F X 5x 2x 4x 14 A Show That The Equation F X 0 Has A Unique Root A In 2 1 B Find The Newton 1 (16.5 KiB) Viewed 37 times
4. Let f(x)=-5x* - 2x² + 4x +14. (a) Show that the equation f(x)=0 has a unique root a in (-2,-1]. = (b) Find the Newton
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4. Let f(x)=-5x* - 2x² + 4x +14. (a) Show that the equation f(x)=0 has a unique root a in (-2,-1]. = (b) Find the Newton
4. Let f(x)=-5x* - 2x² + 4x +14. (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-2) [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, estimate the value of a correct to 4 decimal places. = (25 marks)
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