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CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 2 · Question 5(a)

Let f be a function defined as f(x) = { (sin(ax))/x if x ≠ 0, a ≠ 0; 4 if x = 0 }.

If f is continuous at x = 0, determine the value of a.

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Other parts of this question

  1. 5(b)Using first principles, determine the derivative of f(x) = sin (2x).[6 marks]
  2. 5(c)(i)Show that x dy/dx = y/(1 + x²).[7 marks]
  3. 5(c)(ii)Show that d²y/dx² + (3y)/(1 + x²)² = 0.[8 marks]

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