CAIE P3 2010 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2010
SessionJune
TopicFixed Point Iteration

6 The curve \(y = \frac { \ln x } { x + 1 }\) has one stationary point.
  1. Show that the \(x\)-coordinate of this point satisfies the equation $$x = \frac { x + 1 } { \ln x }$$ and that this \(x\)-coordinate lies between 3 and 4 .
  2. Use the iterative formula $$x _ { n + 1 } = \frac { x _ { n } + 1 } { \ln x _ { n } }$$ to determine the \(x\)-coordinate correct to 2 decimal places. Give the result of each iteration to 4 decimal places.