You can also solve many equations of the form f (x) = x numerically using
Iterate
from
the Calculus submenu. This technique works for functions satisfying
f′(x)
< 1 near the intersection of the curve y = f (x)
and the line y = x. You start with an estimate x0 for the root, and
Iterate returns the list of values
You can generate these numbers geometrically by starting at the point (1, 0) and moving vertically to the curve y = cos x, then horizontally to the line y = x, then vertically to the curve y = cos x, then horizontally to the line y = x, and so forth, as illustrated in the following figure. dtbpF3in2.0003in0pt
This figure can be generated by plotting cos x and x as usual, then selecting the matrix