To show that is the bivariate limit at the origin, find so that .
Consider, then, the following annotated estimate for = .
Consequently, , that is, .
Figure 3.2.13(a) compares with , the first in green, the second, in red. The green surface lies above the red surface, indicating that near the origin, is greater than .
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Figure 3.2.13(a) in red, in green
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Maple corroborates these results by computing the bivariate limit, here accessed through the Context Panel.
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Context Panel: Limit (Bivariate)
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