Homework Help Overview
The discussion revolves around finding an example of a function from R² to R that is continuous at the point (0,0), has partial derivatives at that point, but is not differentiable there. Participants are exploring the properties of such functions and their definitions.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants are attempting to identify specific functions that meet the criteria outlined in the original post. Questions about the definition of continuity at a point and the implications of having partial derivatives without differentiability are raised.
Discussion Status
Some participants have suggested potential functions that may satisfy the requirements, and there is an acknowledgment of one function that appears to work based on a participant's plot. However, there is no explicit consensus on the correctness of the examples provided.
Contextual Notes
Participants are discussing the properties of functions in the context of calculus, particularly focusing on continuity, differentiability, and the behavior of functions around the origin. There may be constraints related to homework guidelines that influence the nature of the discussion.