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Home Partial Differentiation Contionuous Functions of Two or More Variables Examples Example 6
 
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Example 6

Find a set on which h(x, y) = logxy is continuous.

We use the identity

11_partial_differentiation-110.gif

  • ln y is continuous for y > 0.
  • ln x is continuous for x > 0.
  • In y/ln x is continuous for x > 0, ln x ≠ 0, y > 0, that is, x > 0, x ≠ 1, y > 0.
  • logxy is continuous for x > 0, x ≠ 1, y > 0.

Answer logxy is continuous on the set of all (x, y) such that x > 0, x ≠ 1, y > 0 (Figure 11.2.5).

11_partial_differentiation-112.gif

Figure 11.2.5
Home Partial Differentiation Contionuous Functions of Two or More Variables Examples Example 6

Last Update: 2006-11-15