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4 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2 · Question 2(a)(i)

A curve is defined parametrically by x = (3 - 2t)^2, y = t^3 - 2t.

Find dy/dx in terms of t.

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Other parts of this question

  1. 2(a)(ii)Find the gradient of the normal to the curve at the point t = 2.[2 marks]
  2. 2(b)(i)Express (2x + 1) / (x^2(x + 1)) in the form A/x + B/x^2 + C/(x + 1), where A, B, and C are constants.[7 marks]
  3. 2(b)(ii)Hence, evaluate the integral from 1 to 2 of (2x + 1) / (x^2(x + 1)) dx.[7 marks]

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