## Domain, continuity, boundedness of functions

### Task number: 3195

At what point are the following functions defined? Are they continuous? Are they bounded?

#### Variant 1

\(\frac{2xy}{x^2 + y^2}\)

#### Variant 2

\(\cos \frac{1}{xy}\)

#### Variant 3

\(\frac{1}{1-x^2 - y^2}\)

#### Variant 4

\( \ln \sqrt{x^2 + y^2} \)

#### Variant 5

\( \frac{1}{(x-y)^2} \)

#### Variant 6

\( \frac{ \sin xy}{|x| + |y|} \)