a2 z 2 a1 z a0 0 next we consider f z and apply

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: xactly twice the exponent on x. How could we go about approximating this zero without resorting to the ‘Zero’ command of a graphing calculator? We use the Bisection Method. The first step in the Bisection Method is to find an interval on which f changes sign. We know f (1) = −1 and we find f (2) = 29. By the Intermediate Value Theorem, we know the zero of f lies in the interval [1, 2]. Next, we ‘bisect’ this interval and find the midpoint, 1.5. We find f (1.5) ≈ 5.09. This means our zero is between 1 and 1.5, since f changes sign on this interval. Now, we ‘bisect’ the interval [1, 1.5] and find f (1.25) ≈ 0.80, so now we have the zero between 1 and 1.25. Bisecting [1, 1.25], we find f (1.125) ≈ −0.32, which means the zero of f is between 1.125 and 1.25. We continue in this fashion until we have ‘sandwiched’ the zero between two numbers which differ by no more than a desired accuracy. You can think of the Bisection Method as reversing the sign diagram process: instead of...
View Full Document

Ask a homework question - tutors are online