The bisection method
Grab a calculator (or, better, a spreadsheet; there are many free calculators and spreadsheets on the internet). We’re going to use the bisection method to approximate the solution of the equation
on the interval . (If you don’t know the bisection method, click the “bisection method” link above for an explanation).
The left and right endpoints of this interval are given on the first line of the table below, under the headings “Left” and “Right”. Find the midpoint, enter it into the first row under the heading “Mid”. Evaluate the sign of at the left, right, and mid points of the interval, and use the intermediate value theorem to decide which half-interval contains the solution. Enter the left and right endpoints of this half-interval on the second line, and then just repeat the process: enter the midpoint on the second line, determine which half of the interval on the second line contains the solution and enter its endpoints on the third line of the table, and so on ... until the table is completely filled in.
Among the numbers in the table, the midpoint in the last row is the best approximation of the exact solution. The largest possible error in this approximation is the distance from the midpoint to either of the endpoints in the last row.
(Don't round off!)