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6 marksThe Binomial Theorem

CAPE Pure Mathematics Unit 2 · May/June 2022 · Paper 2 · Question 4(a)(i)

Show that the binomial expansion of (1 + 5x)^(1/3) up to and including the term in x³ is 1 + x - 2x² + 6x³.

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Other parts of this question

  1. 4(a)(ii)Hence, by letting x = -1/32, compute an estimate of ³√27.[5 marks]
  2. 4(b)(i)Use the Intermediate Value Theorem to prove that 4eˣ + 2x² - 5 = 0 has a root in the interval [0, 1].[3 marks]
  3. 4(b)(ii)Use four iterations of the interval bisection method to calculate an approximation of the root of 4eˣ + 2x² - 5 = 0 in the interval [0, 1].[6 marks]
  4. 4(b)(iii)Use three iterations of the linear interpolation method to approximate the root of 4eˣ + 2x² - 5 = 0 in the interval (-2, -1).[5 marks]

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