Maths Core WMA01/WMA02: ITERATIVE FORMULA Topical Past Paper Questions

$$ f(x) = 2x^4 + x^2 - 3x + 8 $$ The curve with equation $y = f(x)$ has a single turning point when $x = \alpha$ (a) Show that $\alpha$ is a solution of the equation $$ x = \sqrt[3]{\frac{3-2x}{8}} $$ [3] The iterative formula $$ x_{n+1} = \sqrt[3]{\frac{3-2x_n}{8}} \quad x_1 = 0…

$$ \mathrm{f}(x)=2x^{3}+x-20 $$ (a) Show that the equation $ f(x) = 0 $ can be rewritten as $$ x=\sqrt[3]{a-bx} $$ where a and b are positive constants to be determined. (2) (b) Starting with $ x_{1}=2.1 $ use the iteration formula $ x_{n+1}=\sqrt[3]{a-bx_{n}} $, with the numeric…

$$ \mathrm{f}(x)=\frac{x^{2}}{4}+\ln(2x),\qquad x>0 $$ (a) Show that the equation $ f(x) = 0 $ can be rewritten as $$ x=\frac{1}{2}\mathrm{e}^{-\frac{1}{4}x^{2}} $$ The equation $ f(x) = 0 $ has a root near 0.5 (b) Starting with $x_{1}=0.5$ use the iterative formula $$ x_{n+1}=\f…