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5 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2004 · Paper 2 · Question 5(c)(ii)

Given that y = (x²-1)/(x²+1).

Show that x(x² + 1)dy/dx - 4y = -4/(x² + 1).

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Other parts of this question

  1. 5(a)Evaluate lim (x²-2x-3)/(x²-4x+3) as x approaches 3.[4 marks]
  2. 5(b)Determine the values of x ∈ R for which the function (x+2)/(x(x+1)) is NOT continuous.[3 marks]
  3. 5(c)(i)Find dy/dx in terms of x.[5 marks]
  4. 5(d)By investigating the sign of f'(x), determine the range of real values of x for which x³ - 5x + 3 is decreasing.[8 marks]

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