Graphically find a root of
f(x) = cos(x) - x2
between x=0 and x=1 which is accurate to within 0.00001.
- Choose Beginning Calculus from the initial menu and press
- Use the arrow keys to move to the menu item Graph y = F(x),
- At the prompt F(x) =, enter the formula
cos(x) - x^2
- and use the bounds
- x0 = 0 x1 = 1
- y0 = -1 y1 = 1
- You will then see the graph of this function.
- Press .
- Use the arrow keys to move to Zoom In and press
- You will now see the graph together with a rectangle:
- Using the arrow keys, move the rectangle so that the intersection
of the graph lies in the interior of the rectangle.
- 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.
- Repeat the previous five steps to get the difference between the endpoints
of the domain to be less than 0.00001.
- From the left hand side of the bottom of the screen, the answer is