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Pure Mathematics 2 Coursework Introduction In this coursework, I will be investigating and comparing the use of 3 different numerical methods for finding roots of equations. The numerical methods that I will be using for this coursework are as follows: 1. Change of sign: Decimal search 2. Fixed point iteration: Newton-Raphson Method 3. Rearranging f(x)=0 to the form x=g(x) Change of Sign: Decimal Search For this method I will be using the above equation: x³-4x²-3x+5=0. The first step for this method is to construct a table of values that range the values of the x-axis that the graph passes: x F(x) -5 -205 -4 -111 -3 -49 -2 -13 -1 3 0 5 1 -1 2 -9 3 -13 4 -7 5 15 F(x) changes sign between [-2,-1], [0,1] and [4,5]; indicating that a root lies between each of these x co-ordinates. The next few steps can now be repeated to obtain a more accurate value, taking x1 and x2 to be the lower and upper possible bounds of x. I shall be testing x between 4 and 5. The table below...

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