Edexcel FP1 2013 June — Question 2

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJune
TopicSign Change & Interval Methods
TypeLinear Interpolation Only

2. $$\mathrm { f } ( x ) = \cos \left( x ^ { 2 } \right) - x + 3 , \quad 0 < x < \pi$$
  1. Show that the equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) in the interval \([ 2.5,3 ]\).
    [0pt]
  2. Use linear interpolation once on the interval [2.5,3] to find an approximation for \(\alpha\), giving your answer to 2 decimal places.