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SANGHERA.JAS
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Do I need to use Schwarz's or Young's theorems to prove it, if don't then do I need to evaluate them on (0,0) using definition.
Partial Derivatives: Proving & Evaluating at (0,0)
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SUMMARY
The discussion focuses on the evaluation of partial derivatives at the point (0,0) and the necessity of using Schwarz's or Young's theorems in this context. Participants emphasize the importance of calculating mixed partial derivatives, specifically fxy and fyx, for the given functions. The consensus is that evaluating these derivatives at the origin is essential for proving their equality, which is a fundamental aspect of multivariable calculus.
PREREQUISITES- Understanding of partial derivatives and their notation
- Familiarity with Schwarz's theorem and Young's theorem
- Knowledge of multivariable calculus concepts
- Ability to evaluate limits and derivatives at specific points
- Study the application of Schwarz's theorem in multivariable calculus
- Learn about Young's theorem and its implications for mixed partial derivatives
- Practice evaluating partial derivatives at various points using definitions
- Explore examples of functions where mixed partials are not equal
Students and educators in mathematics, particularly those studying multivariable calculus, as well as professionals needing to apply partial derivative concepts in fields such as physics and engineering.
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