0
.2
4
equals
5
The blue point is the "target" of the limit (at x = a). Note that the orange points are the corresponding places on the axes which give rise to the blue point. The shaded region represents the "neighborhood" within which we want to "capture" the limit. Epsilon (labeled E here) is the vertical distance between the orange point on the y-axis and each of the blue, horizontal-line boundaries of the shaded region. The height of the blue-shaded region is 2*E. Delta (labeled d here) is the horizontal distance between the orange point on the x-axis and each of the red, vertical-line boundaries of the shaded region. The width of the red-shaded region is 2*d.
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