Chapter 3: Functions of Several Variables
Section 3.2: Limits and Continuity
Prove the inequality x3−y3≤x2+y23/2.
The requisite estimates are shown below.
=x x2 + y y2
Inequalities 4 and 5
Figure 3.2.20(a) compares x2+y23/2 with x3−y3, the first in green, the second, in red. The green surface lies above the red surface, indicating that x2+y23/2 is greater than x3−y3.
Figure 3.2.20(a) x3−y3 in red, x2+y23/2 in green
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