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.

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- Nov 23rd 2009, 07:55 PMroninproUniform Continuity
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. - Nov 24th 2009, 02:14 AMFocus
- Nov 24th 2009, 05:43 AMroninpro
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.