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3.7 Numerical methods (A-level only)

3.7 Numerical methods (A-level only)

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Question 86

The equation x3−3x2+5=0x^3 - 3x^2 + 5 = 0x3−3x2+5=0 has exactly one real root.

a.

Show that, for this equation, the Newton-Raphson formula can be written

xn+1=2xn3−3xn2−53xn2−6xn\displaystyle x_{n+1} = \frac{2x_n^3 - 3x_n^2 - 5}{3x_n^2 - 6x_n}xn+1​=3xn2​−6xn​2xn3​−3xn2​−5​

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b.

Using the formula in part (a) with x1=−1x_1 = -1x1​=−1, find the values of x2 x_2\,x2​ and x3x_3x3​. Give your answers to four decimal places.

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c.

Explain why, for this equation, the Newton-Raphson method cannot be used with x1=0x_1 = 0x1​=0.

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Markscheme

3.7 Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7 Numerical methods (A-level only)

125 exam-style questions on CCEA A Level Maths 3.7 Numerical methods (A-level only), covering 3.7.1 Numerical methods (A-level only), 3.7.2 Numerical methods (A-level only), 3.7.3 Numerical methods (A-level only), and 3.7.4 Numerical methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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