Numerical Methods
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Question 41
The diagram shows the part of the graphs of y=23cosecx\displaystyle y = \frac{2}{3}\operatorname{cosec} xy=32cosecx 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=23cosecx\displaystyle y = \frac{2}{3}\operatorname{cosec} xy=32cosecx
b.[1]
Show that x=23cosecx\displaystyle x = \frac{2}{3}\operatorname{cosec} xx=32cosecx has a root between x=2.5x = 2.5x=2.5 and x=3x = 3x=3
c.[3]
Use the diagram, starting with x1=2.6x_1 = 2.6x1=2.6, to determine whether the iteration formula xn+1=23cosecxn\displaystyle x_{n+1} = \frac{2}{3}\operatorname{cosec} x_nxn+1=32cosecxn 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.