Figure 1 below shows the curve y=2xsinxy = 2x\sin xy=2xsinx for 0≤x≤π0 \leq x \leq \pi0≤x≤π, where x x\,x is measured in radians. The maximum point on this curve segment is PPP.
Show that the xxx-coordinate of P P\,P satisfies the equation
tanx+x=0\tan x + x = 0tanx+x=0
Use the Newton-Raphson method, with a suitable initial value, to find the xxx-coordinate of PPP, giving your answer correct to four decimal places. Show the result of each iteration.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.