Edexcel Mathematics June 2018 · Paper 1 · Question 4 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

June 2018 · Paper 1 · Question 4 · 4 marks

4. The curve with equation y = 2 ln(8 − x) meets the line y = x at a single point, x = α. (a) Show that 3 < α < 4 (2) y 4 4xOy = 2 ln(8 − x)y = x Figure 2 Figure 2 shows the graph of y = 2 ln(8 − x) and the graph of y = x. A student uses the iteration formula xn + 1 = 2 ln(8 − xn), n ∈  in an attempt to find an approximation for α. Using the graph and starting with x1 = 4 (b) determine whether or not this iteration formula can be used to find an approximation for α, justifying your answer . (2) 9

Lesson: Locating Roots by Change of Sign