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4 marksDifferentiation I

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

A rectangular box without a lid is made from thin cardboard. The sides of the base are 2x cm and 3x cm, and its height is h cm. The total surface area of the box is 200 cm².

Show that h = 20/x - 3x/5.

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Other parts of this question

  1. 5(a)Use L'Hopital's rule to obtain lim (x→0) (sin 4x / sin 5x).[3 marks]
  2. 5(b)(i)a)Find dy/dx.[4 marks]
  3. 5(b)(i)b)Show that x² dy/dx = y².[2 marks]
  4. 5(b)(ii)Hence, or otherwise, show that x² d²y/dx² + 2(x - y) dy/dx = 0.[3 marks]
  5. 5(c)(ii)Find the height of the box for which its volume V cm³ is a maximum.[9 marks]

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