what is an example where a function neither diverges nor converge?

Question

X is going to infinity and x is also going to negative infinity

Answer 1

One example is the function f(x)=sin(x). As x goes to infinity, f(x) doesn't converge to any specific number and doesn't diverge to infinity.

Answer 2

In my opinion, there are a number of things wrong with this question:

(1) Functions don't really converge/diverge. Sequences and series and integrals are usually where the words converge/diverge are used. Functions are usually said to have a limit.

(2) Diverging is the opposite of converging, so they can't both happen. If a series/sequence/integral oscillates, it diverges.

So if what you are REALLY asking is to find a function that doesn't have a limit as x goes to infinite (neither a finite limit nor an infinite one) then f(x) = sin x works.

Answer 3

f(x) = sin x
or any oscillating function