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Home Partial Differentiation Contionuous Functions of Two or More Variables Examples Example 4
 
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Example 4

Find a set on which h(x, y) = ln(x + y) is continuous. By Theorems 1 and 2,

  • x + y is continuous for all (x, y),
  • ln u is continuous for u > 0,
  • ln(x + y) is continuous for x + y > 0.

Answer ln(x + y) is continuous on the set of all (x, y) such that x + y > 0, shown in Figure 11.2.3.

11_partial_differentiation-105.gif

Figure 11.2.3
Home Partial Differentiation Contionuous Functions of Two or More Variables Examples Example 4

Last Update: 2006-11-15