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5 marksRoots of Equations

CAPE Pure Mathematics Unit 2 · May/June 2021 · Paper 2 · Question 4(d)

Use the iteration x_(n+1) = (sin x_n + 2) / 3 and the initial approximation x = 1 to calculate an approximate value of the root of f(x) = sin x – 3x + 2, correct to 2 decimal places.

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Other parts of this question

  1. 4(a)Determine the first three terms of the expansion of (1 – 8x)^(1/2).[4 marks]
  2. 4(b)Hence, by letting x = 1/100, determine √23.[6 marks]
  3. 4(c)(i)Use the Intermediate Value Theorem to show that the equation 4 sin 2x + x³ – 3 = 0 has a root in the interval [0, 1].[4 marks]
  4. 4(c)(ii)Use three iterations of the interval bisection method to obtain an approximation of the root.[6 marks]

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