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4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by 2.x2 f (x, y) = x2 + y? Show that 0 < f(x, y) < 2

4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by 2.x2 f (x, y) = x2 + y? Show that 0 < f(x, y) < 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Continuity 4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by 2.22 f(x, y) x2 + y? Show that 0 < f(x, y) < 2 for (x, y) E D. 5. Show that the function h(x, y) defined by Vi- i if + y? < 1 1-x2-y? h(x, y) = 0; if a? + y? > 1 is discontinuous.
Transcribed Image Text:Continuity 4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by 2.22 f(x, y) x2 + y? Show that 0 < f(x, y) < 2 for (x, y) E D. 5. Show that the function h(x, y) defined by Vi- i if + y? < 1 1-x2-y? h(x, y) = 0; if a? + y? > 1 is discontinuous.
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