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Change of sign Bisection Success The success of the bisection method can be proved by using the following equation: f(x) = 0.64x4+0.28x2-2x+0.28 For this method, I have chosen to find the root between 0 and 1. Below is the process taken to find this root, each table represents zooming in once (halving the window e.g. first window is 1 unit, second window is 0.5 units). Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound 0.000000 0.500000 1.000000 x 0.000000 0.250000 0.500000 x 0.280000 -0.610000 -0.800000 f(x) 0.280000 -0.200000 -0.610000 f(x) Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound 0.000000 0.125000 0.250000 x 0.125000 0.187500 0.250000 x 0.280000 0.034531 -0.200000 f(x) 0.034531 -0.084365 -0.200000 f(x) Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound 0.125000 0.156250 0.187500 x 0.125000 0.140625 0.156250 x 0.034531 -0.025283 -0.084365 f(x) 0.034531 0.004537 -0.025283 f(x) As to achieve the desired accuracy (of 3 decimal places) this process had to be repeated many times, the last of which is shown below: Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound 0.142975 0.14299 0.143005 x 0.14299 0.142998 0.143005 x 4.14E-05 1.23E-05 -1.7E-05 f(x) 1.23E-05 -2.3E-06 -1.7E-05 f(x) Shown in the lightly shaded area; are the X values for which the first 3 decimal places are the same. From the image above it can be seen that the process has succeeded...

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