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Exercise 1. Define G: R² → R by G(x, y) = 0, if (x, y) = (0,0); x²y x² + y² , if (x, y) = (0,0). 1) Show that G is not continuous at 0 in R². 2) Show that for any line D in R2, the restriction G|D is continuous.

Exercise 1. Define G: R² → R by G(x, y) = 0, if (x, y) = (0,0); x²y x² + y² , if (x, y) = (0,0). 1) Show that G is not continuous at 0 in R². 2) Show that for any line D in R2, the restriction G|D is continuous.

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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Exercise 1 Part 2!
Exercise 1. Define G : R² → R by G(x, y) = , if (x, y) = (0,0); 0 x²y x² + y² if (x, y) = (0,0). 1) Show that G is not continuous at 0 in R². 2) Show that for any line D in R², the restriction G|D is continuous.
Transcribed Image Text:Exercise 1. Define G : R² → R by G(x, y) = , if (x, y) = (0,0); 0 x²y x² + y² if (x, y) = (0,0). 1) Show that G is not continuous at 0 in R². 2) Show that for any line D in R², the restriction G|D is continuous.
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