Problem:
Graphically find a root of

f(x) = cos(x) - x2

between x=0 and x=1 which is accurate to within 0.00001.


Visualization:
Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Graph y = F(x), press and .
  3. At the prompt F(x) =, enter the formula
    cos(x) - x^2
  4. and use the bounds
    x0 = 0 x1 = 1
    y0 = -1 y1 = 1
  5. You will then see the graph of this function.
  6. Press .
  7. Use the arrow keys to move to Zoom In and press and .
  8. You will now see the graph together with a rectangle:

  9. Using the arrow keys, move the rectangle so that the intersection of the graph lies in the interior of the rectangle.
  10. Press and you will see the interior of the rectangle expanded to fill the screen. Note at the left hand side of the bottom of the screen contains the x and y coordinates of the view. In particular, the x coordinates varies between 0.75 and 0.85.
  11. Repeat the previous five steps to get the difference between the endpoints of the domain to be less than 0.00001.

  12. From the left hand side of the bottom of the screen, the answer is 0.82413.