Illustrate graphically the epsilon-delta definition of limits to obtain evidence that

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 functionx^(1/3) - and use the bounds
- x0 = -1 x1 = 1
- y0 = -1 y1 = 1

- You will then see the graph of this function.
- Press and use the arrow keys
to move to
*Zoom In*. Press and . - You will see the following graph with a rectangle (really a square!)
which encloses the area to which the zoom command will take you. This
rectangle corresponds to choosing
*epsilon*= 0.1 and*delta*= 0.1. - Press and the zoomed in graph is
drawn. Clearly,
*delta*= 0.1 does not work. - We'll make the
*delta*smaller by changing the x coordinates. Press and use the arrow keys to*Change [x0,x1]*and press . - Now use the bounds
- x0 = - 0.0005 x1 = 0.0005

- From the following picture, we see that this choice of
*delta*works.