Question

A question of Limits. If f(x) approaches infinity as x approaches infinity, would you say that the limit of f(x) equals infinity or does not exist?

Answer 1

You would notate it like so:
\[\lim_{x\rightarrow\infty}{f(x)}=\infty\]

Answer 2

I know how to notate it, what I am questioning is whether it is correct to have the "limit" of a function as infinity or if that limit wouldn't exist.

Answer 3

Oh I see, well in that case it would not exist.

Consider the following:
\(f(x)=x\)
\(g(x)=2x\)

If you tried notating that it existed, you would have:
\[\lim_{x\rightarrow\infty}{f(x)}=\infty\]
And
\[\lim_{x\rightarrow\infty}{g(x)}=\infty\]
So you would be able to come to the conclusion that:
\[\lim_{x\rightarrow\infty}{f(x)}=\lim_{x\rightarrow\infty}{g(x)}\]
We know this to be incorrect since the two functions are in fact different so therefore, you would say that the limit does not exist