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5 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 2 · Question 5(c)

The equation of an ellipse is given by x = 1-3 cos θ, y = 2 sin θ, 0≤θ≤2π.

Find dy/dx in terms of θ.

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Other parts of this question

  1. 5(a)(i)Find lim (x→2) f(x).[4 marks]
  2. 5(a)(ii)Determine whether f(x) is continuous at x = 2. Give a reason for your answer.[2 marks]
  3. 5(b)Show that dy/dx = (−4x³ – 10x² – 14x + 4) / (x² + 2)⁴[5 marks]
  4. 5(d)(i)Determine the coordinates of the points P and Q at which the curve and the line intersect.[4 marks]
  5. 5(d)(ii)Calculate the area of the shaded region.[5 marks]

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