Page 95 - Calc for the Clueless

Newton's formula becomes

Simplifying, we get

f(1) = -3 and f(2)= 3.

Let's take x 1 = 1.5 for the first approximation. Probably X 1 = 1 or x 1 = 2 would work OK.

Continuuuuuing, we get x 4 = 1.671700271, x 5 = 1.671699882, x 6 = 1.671699882. We have reached the accuracy
of our calculator, nine decimal places, probably more accurate than we would ever need.

Note 1

Sometimes the method doesn't work. A full study is left to other courses.

Note 2

When the method works, it usually works very quickly with great accuracy.

Note 3

This topic, as well as the other two approximations, can be done at many levels. Most appropriately, they occur
in either calc I or II.

Trapezoidal Method