- Thread starter
- #1

- Thread starter highmath
- Start date

- Thread starter
- #1

- Jan 30, 2018

- 368

So the function is "increasing" or "decreasing". But I have no idea what "in infinity" means. In Calculus, "infinity" is not a number- it makes no sense to talk about the value of a function, or any property of a function "in infinity" or "at infinity". We can talk about theWhen have a function and I know by investigation of that it getting "bigger and bigger" or getting "smaller and smaller", how could I know that in infinity it continue by that wayalways?

The most we can say here is that, if a function is increasing, then its limit as x goes to infinity is larger than or equal to any value of the function. If the function is decreasing then its limit as x goes to infinity is less than or equal to any value of the function.

If you are thinking that the limit, as x goes to infinity, of an increasing function must be infinity, that is incorrect. For example, if f(x)= (x- 1)/x= 1- 1/x then f(x) is increasing and the limit as x goes to infinity is 1.

- Thread starter
- #3

If I know that x goes to infinity, so how can I know how thefunction "as x goes to infinity".

.

What the limit help me for?

- Jan 30, 2018

- 368

First, you will have to tell us what **you** mean by "function pattern".

- Thread starter
- #5

So the question is the number theory.

o. k. I will continue with it.

(1)

What axioms I need to prove it?

By what can I use to show that the function is depend on Number Theory?

If I err tell me.

(2)

Is There a calculus way to prove it?

by what means in general?

- Jan 30, 2018

- 368