The problem involves proving the limit \(\lim_{x\to 1^{+}}{\frac{x-3}{x-1}}=-\infty\) using the definition of a limit. The original poster is attempting to establish an inequality to demonstrate this limit, but is encountering difficulties in deriving the necessary conditions.
The discussion is ongoing, with participants seeking clarification on the original poster's attempts. A hint has been provided regarding the manipulation of terms, suggesting a potential avenue for further exploration, but no consensus or resolution has been reached.
The original poster has not fully detailed their reasoning process, which may be contributing to the challenges in understanding their approach. There is an emphasis on adhering to the limit definition in the context of the problem.
scientifico said:I've set up this unequation \frac{x-3}{x-1} < - M to prove the limit using its definition but it doesn't lead to the result 1<x<1+\frac{2}{M+1}