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Numerical Methods

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Question 176

f(x)=ln⁡(2x+1)+x2−5x>−0.5f(x) = \ln(2x + 1) + x^2 - 5 \quad x > -0.5f(x)=ln(2x+1)+x2−5x>−0.5

a.

Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [1.8,1.9][1.8, 1.9][1.8,1.9]

[2]
b.

Find f′(x)f'(x)f′(x)

[3]
c.

Using x0=kx_0 = kx0​=k, where k>−0.5k > -0.5k>−0.5, as a first approximation, apply the Newton-Raphson procedure to find a second approximation, giving your answer in terms of kkk.

[3]
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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