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Exercise 8.6.2: Define f(x, y) := Əxdy [1(1². if (x, y) ‡ (0,0), if (x, y) = (0,0). Show that a) The first order partial derivatives exist and are continuous. b) The partial derivatives and exist, but are not continuous at the origin, and (0,0) ‡ 2 (0,0). əyəx 2²

Exercise 8.6.2: Define f(x, y) := Əxdy [1(1². if (x, y) ‡ (0,0), if (x, y) = (0,0). Show that a) The first order partial derivatives exist and are continuous. b) The partial derivatives and exist, but are not continuous at the origin, and (0,0) ‡ 2 (0,0). əyəx 2²

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 8.6.2: Define xy(x²-x²) f(x, y) = To if (x, y) = (0,0), if (x, y) = (0,0). Show that a) The first order partial derivatives exist and are continuous. əxəy b) The partial derivatives and exist, but are not continuous at the origin, and (0,0) ‡ Əxdy əyəx 2²€ (0,0). əyəx
Transcribed Image Text:Exercise 8.6.2: Define xy(x²-x²) f(x, y) = To if (x, y) = (0,0), if (x, y) = (0,0). Show that a) The first order partial derivatives exist and are continuous. əxəy b) The partial derivatives and exist, but are not continuous at the origin, and (0,0) ‡ Əxdy əyəx 2²€ (0,0). əyəx
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