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Numerical Methods

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Question 4
a.

Sketch the graphs of y=ln⁡xy = \ln xy=lnx and y=12x\displaystyle y = \frac{1}{2x}y=2x1​ for x>0 x > 0\,x>0 on the same axes.

[2]
b.

Explain why the equation ln⁡x=12x\displaystyle \ln x = \frac{1}{2x}lnx=2x1​ has exactly one solution.

[1]
c.

By considering a suitable change of sign, show that the solution to the equation lies between 1.4 and 1.5

[2]
d.

Use the iterative formula xn+1=e12xn\displaystyle x_{n+1} = e^{\frac{1}{2x_n}}xn+1​=e2xn​1​ with x1=1.5x_1 = 1.5x1​=1.5, to find x2,x3 x_2, x_3\,x2​,x3​ and x4x_4x4​, giving your answers to four decimal places.

[2]
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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