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3 marksLimits

CAPE Pure Mathematics Unit 1 · May/June 2008 · Paper 2 · Question 5(a)

This question involves limits, differentiation, and optimization problems.

Use L'Hopital's rule to obtain lim (x→0) (sin 4x / sin 5x).

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Other parts of this question

  1. 5(b)(i)a)Find dy/dx.[4 marks]
  2. 5(b)(i)b)Show that x² dy/dx = y².[2 marks]
  3. 5(b)(ii)Hence, or otherwise, show that x² d²y/dx² + 2(x - y) dy/dx = 0.[3 marks]
  4. 5(c)(i)Show that h = 20/x - 3x/5.[4 marks]
  5. 5(c)(ii)Find the height of the box for which its volume V cm³ is a maximum.[9 marks]

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