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(x²y² – y3 x2 + y2 if (x, y) # (0,0) f(x,y) 0, if (x, y) = (0,0) %3D (a) Determine the existence of lim f(x, y) (x,y)¬(0,0) and evaluate it if it exists. Applying the definition of continuity, explain if f(x,y) is continuous at (0,0). (1 (b) (c) Show that fr(0,0) and f,(0,0) exist and find their value.

(x²y² – y3 x2 + y2 if (x, y) # (0,0) f(x,y) 0, if (x, y) = (0,0) %3D (a) Determine the existence of lim f(x, y) (x,y)¬(0,0) and evaluate it if it exists. Applying the definition of continuity, explain if f(x,y) is continuous at (0,0). (1 (b) (c) Show that fr(0,0) and f,(0,0) exist and find their value.

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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Question 1 Consider the function Zy² – y³ f(x, y) = { x2 + y² if (x, y) # (0,0) 0, if (x, y) = (0,0) (а) Determine the existence of lim (x.y)-(0,0) I (x, y) and evaluate it if it exists. Applying the definition of continuity, explain if f(x, y) is continuous at (0,0). (1 (b) (c) Show that f(0,0) and fy(0,0) exist and find their value. (d) Show that the limit lim (x,y)-(0,0) f:(x, y) does not exist.
Transcribed Image Text:Question 1 Consider the function Zy² – y³ f(x, y) = { x2 + y² if (x, y) # (0,0) 0, if (x, y) = (0,0) (а) Determine the existence of lim (x.y)-(0,0) I (x, y) and evaluate it if it exists. Applying the definition of continuity, explain if f(x, y) is continuous at (0,0). (1 (b) (c) Show that f(0,0) and fy(0,0) exist and find their value. (d) Show that the limit lim (x,y)-(0,0) f:(x, y) does not exist.
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