- #1

- 3

- 0

## Homework Statement

I am required to express in [tex]\varepsilon - \delta[/tex] way what I'm suppose to prove in case [tex]lim_\below{(x \rightarrow \infty)} f(x) = \infty[/tex]

## Homework Equations

None.

## The Attempt at a Solution

So first, intuitively I thought that what this means is that [tex]f(x)[/tex] is bigger than any arbitrary number when [tex]x[/tex] is bigger than any arbitrary number. So I attempted to combine the [tex]\varepsilon - \delta[/tex] definitions of when [tex]x[/tex] tends to infinity and when limit [tex]f(x)[/tex] tends to infinity.

I came up with this:

[tex]lim_\below{(x \rightarrow \infty)} f(x) = \infty[/tex] if for every [tex]M>0[/tex] there exists [tex]N>0[/tex] so that for every [tex]x>M[/tex], [tex]f(x)>N[/tex].

I am unsure of whether it's the correct definition. Anyone can verify that?