Numerical Methods
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223
Question 22
The diagram shows the part of the graphs of y=12cosecx\displaystyle y = \frac{1}{2}\operatorname{cosec} xy=21cosecx 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=12cosecx\displaystyle y = \frac{1}{2}\operatorname{cosec} xy=21cosecx
b.[1]
Show that x=12cosecx\displaystyle x = \frac{1}{2}\operatorname{cosec} xx=21cosecx has a root between x=2.5x = 2.5x=2.5 and x=3x = 3x=3
c.[3]
Use the diagram, starting with x1=2.5x_1 = 2.5x1=2.5, to determine whether the iteration formula xn+1=12cosecxn\displaystyle x_{n+1} = \frac{1}{2}\operatorname{cosec} x_nxn+1=21cosecxn 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.