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8 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 2 · Question 5(c)

A chemical process in a manufacturing plant is controlled by the function M = ut + v/t where u and v are constants. Given that M=-1 when t = 1 and that the rate of change of M with respect to t is 35/4 when t = 2,

find the values of u and v.

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Other parts of this question

  1. 5(a)(i)Find the values of x for which (x³+8)/(x²-4) is discontinuous.[2 marks]
  2. 5(a)(ii)Hence, or otherwise, find lim_{x→-2} (x³+8)/(x²-4).[3 marks]
  3. 5(a)(iii)By using the fact that lim_{x→0} (sin x)/x = 1, or otherwise, find, lim_{x→0} (2x²+4x)/(sin 2x).[5 marks]
  4. 5(b)Find[1 mark]
  5. 5(b)(i)a)lim_{x→1+} f(x)[2 marks]
  6. 5(b)(i)b)the value of the constant p such that lim_{x→1} f(x) exists.[4 marks]
  7. 5(b)(ii)Hence, determine the value of f(1) for f to be continuous at the point x = 1.[1 mark]

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