Capire Finalmente i Limiti in Due Variabili (e la Continuità delle Funzioni)
Discover ClearMath Academy🏆 ▶ https://clearmath.it/ 📩IF YOU WANT A LESSON WITH ME📩▶ email me at [email protected] 📜FOR ANALYSIS AND PHYSICS FORMULAS AND DIAGRAMS📜▶ • Post 🚀🚀 IF YOU WANT TO SUPPORT THE CHANNEL WITH €1 🚀🚀 ▶ https://www.paypal.com/donate/?hosted... #mathematics #analysis #functions #limits #theorem #comparison How do you do exercises on limits in two variables? What does it mean that the limit of a function in two variables does not exist, or that it depends on the direction (parameterization)? Today we'll give a visual demonstration of how to solve exercises on one of the most abstract topics in all of Calculus II, if not in all of advanced mathematics, but also among the most important, since all subsequent topics (differentiability, double integrals, etc.) depend on it. We'll see what it means for a limit to not exist, how to verify its existence with the comparison theorem and polar coordinates, and also how to verify whether a function is continuous at a point or has a discontinuity of the third kind. We'll also do an exercise together where we recall notable exponential limits and polar coordinates. Finally, we'll see that the existence of a limit does not guarantee the continuity of a function: we'll delve into the concept of continuity extension to understand when a function in two variables is continuous. This will be a very practical and enlightening video for your Calculus II exam preparation, so don't miss it! 00:00-00:27 Definition of the existence of a limit for functions of one variable 00:27-01:21 When the limit of a function of more than one variable does not exist (because it depends on the direction) 01:21-03:34 How to use the comparison theorem to solve exercises on limits in two variables 03:34-05:05 Solved exercise on limits in two variables (remarkable limit and polar coordinates) 05:05-06:20 How to determine if a function is continuous (discontinuity of the third kind and extension by continuity) Happy studying! -Marco, ClearMath
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