Let $\displaystyle 0 \leq f(x)$

Then proof existence of infinity or a limit (but not both):

Thus,

$\displaystyle \lim c \rightarrow \infty f(x)=L $

or

$\displaystyle \lim c \rightarrow \infty f(x)=\infty$

Logic caution:

In the problem you have to proof that exactly one of the conditions must be satisfied and exactly one.