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5 marksLimits

CAPE Pure Mathematics Unit 1 · 2021 · Paper 2 · Question 6(a)(i)

A function f is defined as f(x) = { 2x + 3; x < 1, 2; x = 1, (x² - 1)/(x - 1); x > 1 }.

Determine whether or not the lim (x→1) f(x) 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)Determine dy/dx in terms of θ.[4 marks]
  3. 6(c)Calculate ∫₁² [f(x) + g(x)] dx.[4 marks]
  4. 6(d)(i)Solve the differential equation dy/dx = sin x / sin y given that when x = 0, y = π/2.[6 marks]
  5. 6(d)(ii)Determine the equation of the curve that passes through (1, 5) and for which y = ∫ 6x² dx.[4 marks]

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