Numerical Methods
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Question 156
The curve with equation y=ln(5−x)y = \ln(5 - x)y=ln(5−x) meets the line y=xy = xy=x at a single point, x=αx = \alphax=α.
a.[2]
Show that 1<α<21 < \alpha < 21<α<2
b.[3]
The diagram shows the graph of y=ln(5−x)y = \ln(5 - x)y=ln(5−x) and the graph of y=xy = xy=x. Use the diagram, starting with x1=kx_1 = kx1=k, where 1<k<21 < k < 21<k<2, to determine whether the iteration formula xn+1=ln(5−xn)x_{n+1} = \ln(5 - x_n)xn+1=ln(5−xn) can be used to find an approximation for α \alpha\,α for all such kkk, justifying your answer in terms of kkk.
Numerical Methods Questions
329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.