Numerical Methods
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223
Question 138
The curve with equation y=ln(6−x)y = \ln(6 - x)y=ln(6−x) meets the line y=xy = xy=x at a single point, x=αx = \alphax=α.
The diagram shows the graph of y=ln(6−x)y = \ln(6 - x)y=ln(6−x) and the graph of y=xy = xy=x. Show that 1<α<2 1 < \alpha < 2\,1<α<2 and use the diagram, starting with x1=2x_1 = 2x1=2, to determine whether the iteration formula xn+1=ln(6−xn)x_{n+1} = \ln(6 - x_n)xn+1=ln(6−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.