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5 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 2 · Question 5(b)(i)

The curve y = hx² + k/x passes through the point P (1,1) and has a gradient of 5 at P.

the values of the constants h and k

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Other parts of this question

  1. 5(a)(i)State the value of lim (as δx → 0) (sin 8x / δx).[1 mark]
  2. 5(a)(ii)Given that sin 2(x + δx) – sin 2x = 2 cos A sin B, find A and B in terms of x and/or δx.[2 marks]
  3. 5(a)(iii)Hence, or otherwise, differentiate with respect to x, from first principles, the function y = sin 2x.[7 marks]
  4. 5(b)Find[1 mark]
  5. 5(b)(ii)the equation of the tangent to the curve at the point where x = 1/2.[5 marks]

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