Continuity of a two-variable function

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Homework Statement



Capture.JPG


Homework 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.

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.
 
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  • #2
LCKurtz
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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].
 
  • #3
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Thank you
 

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