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2 marksLimits

CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 2 · Question 5(b)(ii)

The function f on R is defined by f(x) = {3x-7, if x>4; 1+2x, if x≤4}.

Deduce that f(x) is discontinuous at x = 4.

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Other parts of this question

  1. 5(a)(i)Find lim x→3 of (x²-9) / (x³-27).[4 marks]
  2. 5(a)(ii)Find lim x→0 of (tan x - 5x) / (sin 2x - 4x).[5 marks]
  3. 5(b)(i)a)Find lim x→4⁺ of f(x).[2 marks]
  4. 5(b)(i)b)Find lim x→4⁻ of f(x).[2 marks]
  5. 5(c)(i)Evaluate ∫ from -1 to 1 of (x - 1/x)² dx.[6 marks]
  6. 5(c)(ii)Using the substitution u = x² + 4, or otherwise, find ∫ of x / √(x² + 4) dx.[4 marks]

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