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Numerical Methods

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Question 63

A first-hump curve on x and y axes rises from the origin to a marked maximum P and falls to the positive x-axis at π/4.

The diagram shows the part of the curve y=2xsin⁡4xy = 2x \sin 4xy=2xsin4x. The maximum point on the curve is denoted by PPP.

a.

Show that the xxx-coordinate of P P\,P satisfies the equation tan⁡4x+4x=0\tan 4x + 4x = 0tan4x+4x=0

[3]
b.

Use the Newton-Raphson method, with a suitable initial value, to find the xxx-coordinate of PPP, giving your answer correct to 4 decimal places. Show the result of each iteration.

[4]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Maths
  3. /Numerical Methods

329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

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