Consider the function
Illustrate graphically the epsilon-delta definition of limits to show that f is not continuous at x = 0.
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
- At the prompt F(x) =, enter the function
x^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