Numerical Methods
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Question 119
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]
Let f(x)=ln(5−x)−xf(x) = \ln(5 - x) - xf(x)=ln(5−x)−x. Calculate f(1)f(1)f(1) and f(2)f(2)f(2).
b.[2]
Hence show that 1<α<21 < \alpha < 21<α<2
c.[2]
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=2x_1 = 2x1=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\alphaα, justifying your answer.
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.