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Rudin Ch 4, p. 99 #7. If E ? X and if f is a...

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Advance Math

Rudin Ch 4, p. 99 #7. If E ? X and if f is a function defined onX, the restriction of f to E is the function g whose domain ofdefinition is E, such that g(p) = f (p) for p ? E. Define f and gon ?2 by: f (0, 0) = g(0, 0) = 0, f (x, y) = € xy 2 x 2 + y 4 ,g(x, y) = € xy 2 x 2 + y 6 if (x, y) ? (0, 0). Prove that f isbounded on ?2 , that g is unbounded in every neighborhood of (0, 0)and that f is not continuous at (0, 0); nevertheless, therestrictions of both f and g to every straight line in ?2 arecontinuous! .Explain step by step in detal

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