The discussion revolves around proving a relationship between two functions using the Limit Comparison Theorem, specifically addressing the implication that if f(x) is less than or equal to g(x), then the limit of f(x) should be less than or equal to the limit of g(x).
The discussion is active, with participants exploring different angles on the problem. Some guidance has been offered regarding proof techniques, and there is an ongoing examination of the assumptions related to the limits and their values.
There is a noted confusion regarding the relationship between limits and the range of function values, which remains unresolved in the discussion.
HallsofIvy said:I am puzzled by phind's question. The answer is "yes, it does" but I don't see how that helps here.
QUOTE]
Hm ... I guess I'm missing something. I don't see how the limit of a function could possibly give you a value that is outside the range of the possible values of the function.
Hm ... I guess I'm missing something. I don't see how the limit of a function could possibly give you a value that is outside the range of the possible values of the function.
LCKurtz said:Try ##\lim_{x\to\infty}\frac 1 x##.