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