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6 marksRoots of Equations

CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 3(a)

Module 2 focuses on Roots of Equations, Sequences, Series, and The Binomial Theorem.

Use two iterations of the Newton-Raphson method, with the initial estimate x₀ = 0.3, to calculate a new estimate for the root of f(x) = 3x² - 4x + 1.

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  1. 3(b)Determine the Taylor series expansion of f(x) = 1/(1-2x) about x = 3 up to and including the term in x².[9 marks]
  2. 3(c)(i)Obtain the binomial expansion of (16-5x)¹/⁴ up to and including the term in x².[6 marks]
  3. 3(c)(ii)Hence, state the values for which the expansion of (16 – 5x)¹/⁴ is valid.[2 marks]
  4. 3(c)(iii)Use the expansion obtained in (c)(i) to estimate the value of (16 – 5x)¹/⁴ when x = 3.[2 marks]

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