- #1
IdanH14
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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?