The discussion revolves around the behavior of a function \( f(x) \) as \( x \) approaches infinity, particularly in the context of an integral involving \( f(x) \). Participants are exploring the conditions under which \( f(x) \) approaches zero and the implications of this behavior.
The discussion is ongoing, with participants seeking clarification on the definitions and conditions involved. Some have offered guidance on the need to demonstrate both existence and convergence of the limit, while others are still trying to understand the original question and its context.
There is some confusion regarding the notation and the specific limits being discussed, particularly the introduction of \( n \) and its relevance to the limit of \( f(x) \). Participants are also addressing the need for clearer definitions of convergence and limits in this context.
NateTG said:What you've written doesn't really make sense. What is this question from and about?
Math_Frank said:The Question is
Given the integeral
f(t) = \int_{t}^{2t} e^{-x^2} dx then prove that if f(x) \to 0 then
n \to \infty
Isn't that convergens or it simply existence of the limit?
NateTG said:Where does n come from?
Do you mean "\lim_{x \rightarrow \infty} f(x)=0" when you write "f(x) \to 0"