Numerical Methods
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Question 124
The diagram shows the part of the graphs of y=cosecxy = \operatorname{cosec} xy=cosecx and y=xy = xy=x.
a.[2]
Write down the coordinates of the minimum point and the equations of the two vertical asymptotes for y=cosecxy = \operatorname{cosec} xy=cosecx
b.[1]
Show that x=cosecxx = \operatorname{cosec} xx=cosecx has a root between x=2.6x = 2.6x=2.6 and x=2.9x = 2.9x=2.9
c.[3]
Use the diagram, starting with x1=2.6x_1 = 2.6x1=2.6, to determine whether the iteration formula xn+1=cosecxnx_{n+1} = \operatorname{cosec} x_nxn+1=cosecxn can be used to find an approximation for this root, 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.