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3 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2 · Question 1(a)(i)

The diagram shows points P(p, 0.368) and R(3.5, r) on f(x) = e^x for x in R.

Copy the diagram and on the same axes, sketch the graph of g(x) = ln x.

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Other parts of this question

  1. 1(a)(ii)Describe clearly the relationship between f(x) = e^x and g(x) = ln x.[3 marks]
  2. 1(a)(iii)a)Using a calculator, find the value of r.[1 mark]
  3. 1(a)(iii)b)Using a calculator, find the value of p.[2 marks]
  4. 1(b)Given that log_a(bc) = x, log_b(ca) = y, log_c(ab) = z and a != b != c, show that a^x b^y c^z = (abc)^2.[3 marks]
  5. 1(c)Find the values of x in R for which e^x + 3e^(-x) = 4.[8 marks]

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