Homework Help: Continuity of a two-variable function

1. Jun 19, 2010

oplik

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. Jun 19, 2010

LCKurtz

Hint for (b): Look at

$$\left| \frac{(2x+y)^3+x^2+y^2}{x^2+y^2} - 1\right|$$

Simplify it and change it to polar coordinates. Think about $r\rightarrow 0$.

3. Jun 20, 2010

Thank you