Example 3-2-21 - Maple Help



Chapter 3: Functions of Several Variables



Section 3.2: Limits and Continuity



Example 3.2.21



 Show that for  the bivariate limit at the origin is zero, but both  of the iterated limits $\underset{y\to 0}{lim}\left(\underset{x\to 0}{lim}f\right)$ and $\underset{x\to 0}{lim}\left(\underset{y\to 0}{lim}f\right)$ fail to exist. Hint: Show $\left|f\right|$$\le \left|x\right|+\left|y\right|\le 2\sqrt{{x}^{2}+{y}^{2}}$.