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5 marksLimits

CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2 · Question 5(a)(ii)

A function f is defined as f(x) = (x + 4)^3 for x < -2; f(x) = -10 for x = -2; f(x) = x^2 + 8x - 1 for x > -2.

Determine lim_{x -> -2} f(x).

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Other parts of this question

  1. 5(a)(i)Determine f(-2).[1 mark]
  2. 5(a)(iii)Hence, or otherwise, determine whether f is continuous at x = -2.[1 mark]
  3. 5(b)Evaluate lim_{theta -> 0} (sin theta / sin 4 theta).[4 marks]
  4. 5(c)(i)Determine the stationary points of g and the nature of the stationary points.[9 marks]
  5. 5(c)(ii)Hence, or otherwise, sketch the graph of g showing its intercepts, stationary points and any other important features on the provided grid.[5 marks]

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