Geometric Approach

In geometric terms, the ε, δ condition says that for every horizontal strip (of width 2ε) centered at L, there exists a vertical strip (of width 2δ) centered at c such that whenever x ≠ c is in the vertical strip, f(x) is in the horizontal strip. The graphs in Figure 5.8.2 indicate various horizontal strips and corresponding vertical strips. They should be examined closely.

Figure 5.8.2