Here is a Maple Worksheet graphically and computationally investigating the three delta values described above using an epsilon value of 0.01.

You could graphically demonstrate the failure of a delta value of epsilon/10 to satisfy the limit definition at the upper right corner where epsilon equals 0.01 by graphing y = x² +4 on your graphing calculator with a window setting of

xmin = 5.000999

xmax = 5.001

ymin = 29.00999

ymax = 29.01