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Provide an example of a function of two variables with the desired properties (with justification), or explain why such a function does not exist. A function f(x, y) such that lim (x,mx)→(0,0) f(x, mx) = 0 and lim (x,x²)→(0,0) f(x, x²) = 1 and lim (x,y)→(0,0) f(x, y) exists.

Provide an example of a function of two variables with the desired properties (with justification), or explain why such a function does not exist. A function f(x, y) such that lim (x,mx)→(0,0) f(x, mx) = 0 and lim (x,x²)→(0,0) f(x, x²) = 1 and lim (x,y)→(0,0) f(x, y) exists.

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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Provide an example of a function of two variables with the desired properties (with justification), or explain why such a function does not exist. A function f(x, y) such that lim (x,mx)→(0,0) F(х, тх) —D 0 and lim (x,x²)→(0,0) f(x, x²) = 1 and lim (x,y)→(0,0) f(x, y) exists.
Transcribed Image Text:Provide an example of a function of two variables with the desired properties (with justification), or explain why such a function does not exist. A function f(x, y) such that lim (x,mx)→(0,0) F(х, тх) —D 0 and lim (x,x²)→(0,0) f(x, x²) = 1 and lim (x,y)→(0,0) f(x, y) exists.
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