The discussion revolves around proving that a continuous function \( f(x) \) is bounded on the interval \([a, +\infty)\) given that the limit of \( f(x) \) exists as \( x \) approaches \( +\infty \).
Some participants have offered insights into the relationship between the limit and boundedness, while others are seeking clarification on specific choices made in the reasoning process. The conversation appears to be productive, with various interpretations being explored.
There is a mention of potential confusion regarding the interval of boundedness and the specific choice of epsilon in the limit definition. Participants are also considering the implications of continuity on boundedness.
sedaw said:need to prove that f(x) bounded if f(x) continuous in [a,+infinite] and if there's a limit while x goes to +infinite.
I would really appreciate any kind of help !