Use the bisection method to find a root of the function
f(x) = cos(x) - x.
Since f(0) > 0 and f(1) < 0, we use the bisection method
on the closed interval [0,1].
- At the main menu, use the arrow keys to move to 2. Root (Root finding
by Newton, bisection or secant) and press .
- At the prompt for method, type in b for the bisection
- At the prompt for function, type:
cos(x) - x
- Enter the bounds:
Xmin = 0 Xmax =
One advantage of this program is that at this point the function
evaluated at Xmin and Xmax need not have opposite signs.
- Press .
- At the prompt, Number of digits accuracy, type 6
- and press to draw the graph.
- At this point, you will see the graph and you will be prompted
to enter the left hand endpoint of the subinterval to use; type 0
and, at the prompt for the right hand
endpoint, type 1 .
- You will now see the program subdivide the interval and
pick the appropriate subinterval. This process continues until the
subinterval is too small to visualize and the program then rescales
the coordinates. The endpoints of the subintervals together with
the midpoint are shown at the left of the screen. A copy of one of
the screens is
- Press to return to the screen at which
you entered the endpoints of the first subinterval. You could try to find
another root of the function at this time. Press to return to the screen at which you entered the function.
If you press and Y you will return to the