Hello, I have been asked to show that the function
$\displaystyle f(x,y)=\ln(1+x^2+y^2)$
is uniformly continuous on $\displaystyle \mathbb{R}^2$.
I played with it quite a bit and it is a complete mess. Any suggestions would be appreciated.
Hello, I have been asked to show that the function
$\displaystyle f(x,y)=\ln(1+x^2+y^2)$
is uniformly continuous on $\displaystyle \mathbb{R}^2$.
I played with it quite a bit and it is a complete mess. Any suggestions would be appreciated.
Thank you for the reply.
Although I can see that proving that $\displaystyle g(x,y)$ and $\displaystyle \ln(x)$ are both continuous implies that $\displaystyle \ln(g(x,y))$ is continuous, I do not see why it necessarily implies that it is uniformly continuous.