AQA FP3 2006 June — Question 5

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2006
SessionJune
TopicSequences and series, recurrence and convergence
5
  1. Show that \(\lim _ { a \rightarrow \infty } \left( \frac { 3 a + 2 } { 2 a + 3 } \right) = \frac { 3 } { 2 }\).
  2. Evaluate \(\int _ { 1 } ^ { \infty } \left( \frac { 3 } { 3 x + 2 } - \frac { 2 } { 2 x + 3 } \right) \mathrm { d } x\), giving your answer in the form \(\ln k\), where \(k\) is a rational number.
    (5 marks)
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