Example from Wikipedia.
$f(x)=(x_{1}-x_{2})^2$
Who can it bee shown that the function is not radially unbounded.
$l=lim_{x \to \infty}min_{||x||=r}[(x_{1}-x_{2})^2]$
by using $min_{||x||=r}$ as a step before taking the limit or done step by step.
who do you read $min||x||=r[f(x)]$ is it possible to check first $(x1,0)$, $(0,x2)$ and at the end $x1=x2$ $(x1,x1)$?
Let $x=(x_1,x_2)$ such that $||x||=r$ If $x_1=x_2$, then $(x_1-x_2)^2 =0.$ Hence
$$ \min_{||x||=r}[(x_{1}-x_{2})^2]=0.$$
This gives
$$l=0.$$