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12. Consider the function (z-y)2 f(x,y) = { if (x, y) = (0,0) if (x, y) = (0,0) a) Does lim(z.y)→(0,0) f(x, y) exist? Justify your answer. b) Is f continuous at (0,0)? Justify your answer. af af c) Compute of (0,0), 3 (0,0), if they exist there. (Hint: You will need to Əy use the limit definition of the partial derivative.)

12. Consider the function (z-y)2 f(x,y) = { if (x, y) = (0,0) if (x, y) = (0,0) a) Does lim(z.y)→(0,0) f(x, y) exist? Justify your answer. b) Is f continuous at (0,0)? Justify your answer. af af c) Compute of (0,0), 3 (0,0), if they exist there. (Hint: You will need to Əy use the limit definition of the partial derivative.)

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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12. Consider the function f(x,y) = { 1²+y² if (x, y) = (0,0) if (x, y) = (0,0) a) Does lim(z.y)+(0,0) f(x, y) exist? Justify your answer. b) Is f continuous at (0,0)? Justify your answer. af c) Compute of (0,0), of (0,0), if they exist there. (Hint: You will need to Əy use the limit definition of the partial derivative.)
Transcribed Image Text:12. Consider the function f(x,y) = { 1²+y² if (x, y) = (0,0) if (x, y) = (0,0) a) Does lim(z.y)+(0,0) f(x, y) exist? Justify your answer. b) Is f continuous at (0,0)? Justify your answer. af c) Compute of (0,0), of (0,0), if they exist there. (Hint: You will need to Əy use the limit definition of the partial derivative.)
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