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4 marksLimits

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

A function f is defined as: f(x) = (x²-1)/(x-1) for x < 1 f(x) = 4x for x > 1 f(x) = 2 for x = 1.

Determine whether or not the limit of f at x = 1 exists.

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Other parts of this question

  1. 6(a)(ii)Determine whether f is continuous at x = 1.[2 marks]
  2. 6(b)(i)Determine (d/dθ)g(x), in terms of θ.[3 marks]
  3. 6(b)(ii)Determine the equation of the normal to the curve at the point (√3, 5/2).[8 marks]
  4. 6(c)(i)Formulate an appropriate differential equation and find the equation of the curve family.[5 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]

More practice: the rest of this paper · more Limits questions · all CAPE Pure Mathematics Unit 1 past papers