Coursework.Info - Inspiration in an Instant

On the left is an image preview of every page of this document, and below are the first 150 words with formatting removed:

Pure Mathematics 2 Coursework Change of sign method --- interval bisection method Introduction: When I am looking for the roots of the equation, actually what I want is the values of x for which the graph y=f(x) crosses the x-axis. As the graph f(x) crosses the x-axis, there is going to be a sign change of y value on the two sides of the root. Hence provided the function gives a continuous graph, if there is a sign change in a located interval, I will know that the interval contains one root. For interval bisection method, what I am actually going to do is to divide the interval into two parts, then take the half which contains sign changes of y. Y=(x-2)(x-4)(x-6)+1 From the graph we can see that there are three roots lying in the interval (1,2); (4,5); (5,6). I am going to focus on the root lying in the interval (1,2) I will...

To see the full version of this document, and 145,348 others