ABSTRACT
In the method of bisection the mid-point of the interval, i.e. x 3 = x 1 + x 2 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq1200.tif"/> , is taken, and from the sign of f(x3) it can be deduced whether a root lies in the half interval to the left or right of x3. Whichever half interval is indicated, its mid-point is then taken and the procedure repeated. The method often requires many iterations and is therefore slow, but never fails to eventually produce the root. The procedure stops when two successive values of x are equal, to the required degree of accuracy.
Application: Using the bisection method, determine the positive root of the equation x + 3 = e x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq1201.tif"/> , correct to 3 decimal places
