Erratum SW 3-2 Answer Key Item 2c
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Erratum SW 3-2 Answer Key no. 2c The ln function is only continuous at all points in its domain. Thus, the possible points of discon- tinuity occur at (x, y) where xy 2 ≤ 0. But xy 2 ≤ 0 ⇔ y = 0 or x ≤ 0. Since all open balls centered at (0, 0) will contain some points for which x ≤ 0, we cannot even speak of the limit of f (x, y) as (x, y) → (0, 0) (Please see definition of limit of a function of 2 variables.). Thus the limit does not exist for all points in the set S = {x, y) | y = 0 or x ≤ 0}. Consequently, f has an essential discontinuity at all points in this set.
Transcript of Erratum SW 3-2 Answer Key Item 2c
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Erratum SW 3-2 Answer Key no. 2c
The ln function is only continuous at all points in its domain. Thus, the possible points of discon-
tinuity occur at (x, y) where xy2 0. But xy2 0 y = 0 or x 0. Since all open balls centeredat (0, 0) will contain some points for which x 0, we cannot even speak of the limit of f(x, y) as(x, y) (0, 0) (Please see definition of limit of a function of 2 variables.). Thus the limit does not existfor all points in the set S = {x, y) | y = 0 or x 0}. Consequently, f has an essential discontinuity atall points in this set.
