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Homework Help: Bounded functions

  1. Aug 25, 2010 #1
    1. The problem statement, all variables and given/known data

    This is from baby rudin:

    If [tex] E\subset X[/tex] and if f is a function defined on X, the restriction of f to E is the function g whose domain of definition is E, such that [tex] g(p)=f(p)[/tex] for [tex]p\in E[/tex]. Define f and g on R^2 by: [tex]f(0,0)=g(0,0)=0[/tex], [tex]f(x,y)=\frac{xy^2}{x^2+y^4}, g(x,y)=\frac{xy^2}{x^2+y^6}[/tex] if [tex](x,y)\neq (0,0)[/tex]. Prove that f is bounded on R^2, that g is unbounded in every neighborhood of [tex](0,0)[/tex], and that f is not continuous at (0,0); nevertheless, the restrictions of both f and g to every straight line in R^2 are continuous.

    2. Relevant equations

    In the question statement

    3. The attempt at a solution

    This is after the continuity chapter and before the differentiation chapter, so I am clueless here. I was thinking of bounding the function by another function but didn't get anywhere. Anyone wanna help?

    Thanks,
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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