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2 marksLimits

CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2 · Question 5(b)(i)b)

A function g is defined as g(x) = 2x + 1 for x < 1, and g(x) = 3x for x ≥ 1.

Determine lim_{x → 1} g(x).

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Other parts of this question

  1. 5(a)(i)a)Determine the value of lim_{x → -5⁺} f(x).[1 mark]
  2. 5(a)(i)b)Determine the value of lim_{x → 5} f(x).[1 mark]
  3. 5(a)(ii)State the value of k such that lim_{x → k} f(x) = -2.[1 mark]
  4. 5(b)(i)a)Determine g(1).[1 mark]
  5. 5(b)(ii)Hence, state whether g is continuous at x = 1. Give a reason for your answer.[2 marks]
  6. 5(c)Given that y = (2x³ + 4)⁷ and x = 1 - 2t, determine dy/dt.[5 marks]
  7. 5(d)Determine f'(x), using first principles, given that f(x) = sin x.[6 marks]
  8. 5(e)Determine ∫₂⁴ x(x - 4)⁵ dx using the substitution u = x - 4.[6 marks]

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