Example 5

Find a set on which h(x,y) = x^y + cosis continuous.

• x^y is continuous for x > 0.
• x² is continuous for all x.
• x² - y is continuous for all (x, y).
• is continuous for x² - y > 0.
• cos is continuous for x² - y > 0.
• x^y + cos is continuous for x > 0 and x² - y > 0.

Figure 11.2.4

Answer h(x, y) is continuous on the set of all (x, y) such that x > 0 and x² - y > 0. The set is shown in Figure 11.2.4.