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Homework Help: Continuity of a two-variable function

  1. Jun 19, 2010 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    My main problem is connected with b/ and d/. I found a formula involving the norm of the function, but I'm not sure if it's a good idea using it.

    3. The attempt at a solution

    I can prove that a function is not continuous by finding different values for x and y for which the limit at the point is approaching different values, but have no idea how to prove that it is continuous.
    Last edited: Jun 19, 2010
  2. jcsd
  3. Jun 19, 2010 #2


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    Hint for (b): Look at

    [tex]\left| \frac{(2x+y)^3+x^2+y^2}{x^2+y^2} - 1\right| [/tex]

    Simplify it and change it to polar coordinates. Think about [itex]r\rightarrow 0[/itex].
  4. Jun 20, 2010 #3
    Thank you
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