Solution of Equations by numerical methods

... MEI PURE 2 COURSEWORK SOLUTION OF EQUATIONS BY NUMERICAL METHODS 1. Change of Sign Method This method makes use of the fact f(x) changes sign at a root of an equation. f(x) must be a continuous function i.e. it must not have any asymptotes or other breaks in it. Once an interval in which f(x) changes sign is located, we know that that interval contains a root. It is best to sketch the diagram of f(x) first so that we can see how many roots the equation has and their approximate positions. Decimal Search The equation that will be investigated here is f(x) = 4x3+5, a diagram of which is shown below. From the graph we can see that there is only one root. Zooming in, as shown below, we can also see that this root lies between X=-1 and X=-2 Taking increments in x of 0.1 within the interval [-2, -1] and working out the value

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