Mathematics Pure WMA11: Numerical methods Topical Past Paper Questions

$$ \mathrm{g}(x)=3x-5+5\sin\left(x^{2}\right) $$ where x is measured in radians. (a) Show that $ g(x)=0 $ has a root $ \alpha $ in the interval [0.7, 0.8] (2) (b) Show that the equation $ g(x)=0 $ can be written in the form $$ x=\left[\arcsin\left(1-px\right)\right]^{\frac{1}{2}}…

A continuous curve has equation $$ y=\mathrm{e}^{-x^{2}}\sin3x\qquad0\leqslant x\leqslant\frac{\pi}{3} $$ The curve has a stationary point at the point P. (a) Show, using calculus, that the $x$ coordinate of $P$ is a solution of the equation $$ x=\frac{1}{3}\arctan\left(\frac{3}{…

Figure 4 Figure 4 is a graph showing the path of a golf ball after the ball has been hit until it first hits the ground. The vertical height, h metres, of the ball above the ground has been plotted against the horizontal distance travelled, x metres, measured from where the ball…