Graphically find a root of

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

Using Microcalc:

- Choose
*Beginning Calculus*from the initial menu and press . - Use the arrow keys to move to the menu item
*Graph y = F(x)*, press and . - At the prompt
*F(x) =*, enter the formulacos(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 and . - 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 0.82413.