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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2018 · Paper 2 · Question 6(c)(i)

The slope of a tangent of the curve, g, at any point (x, y) is equal to the product of the x-coordinate and the reciprocal of the y-coordinate of the point of tangency.

Formulate an appropriate differential equation and find the equation of the curve family.

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Other parts of this question

  1. 6(a)(i)Determine whether or not the limit of f at x = 1 exists.[4 marks]
  2. 6(a)(ii)Determine whether f is continuous at x = 1.[2 marks]
  3. 6(b)(i)Determine (d/dθ)g(x), in terms of θ.[3 marks]
  4. 6(b)(ii)Determine the equation of the normal to the curve at the point (√3, 5/2).[8 marks]
  5. 6(c)(ii)Hence, or otherwise, determine the equation of the curve given that it passes through the point (1, 3).[13 marks]

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