Consider the function

Illustrate graphically the epsilon-delta definition of limits to show that **f** is not continuous at **x = 0**.

Using Microcalc:

There is a built-in function which will let us construct the function *f*

- 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^2 + 0.002 step(x) - and use the bounds
- x0 = -1 x1 = 1
- y0 = -1 y1 = 1

- You will then see the graph of this function. It appears that this
function is continuous at
*x*= 0. - 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. - Repeat the last two steps several times until you obtain the following
graph. The rectangle indicates that there is a problem when choosing
*epsilon*= 0.001