Homework Help Overview
The discussion revolves around the evaluation of a limit equation involving the expression \(\lim _{(x,y)\to (\infty,0)} \frac{1}{(x-y)^{x}}\). Participants are examining the validity of different interpretations and the reasoning behind the original poster's conclusion that the limit equals 1.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- The original poster questions why their interpretation of the limit as 1 is considered incorrect, exploring the equivalence to forms like \(1 - \infty^{-\infty}\) and \(1 - \text{infinitesimal}\). Some participants assert that the limit approaches 0 instead, discussing the behavior of \((x-y)^{x}\) as \(x\) approaches infinity.
Discussion Status
Participants are actively engaging with the problem, with some providing insights into the nature of the limit and questioning the assumptions made by the original poster. There is no explicit consensus on the correct interpretation, but there is a productive exchange of ideas regarding the limit's behavior.
Contextual Notes
The original poster expresses uncertainty about their reasoning and seeks clarification on the logic behind their answer being deemed incorrect. There is an emphasis on the need for clearer mathematical expressions, as noted by one participant's suggestion to use LaTeX for posting equations.
I'm glad that