Limits are...weird...for multi-variable functions | Limits along paths
In single variable calculus, you only had to take a limit from the left and from the right. In multi variable calculus, you can approach from every single direction. One way to say a limit doesn't exist is then to find two different paths where along those two different paths the limit approaches different values. Then for sure the limit of the function does not exist. However, you could find 10,100,1000 paths where the limit was the same along every path and yet the limit still didn't exist because you just hadn't found the one path that was weird yet. This is problematic and motivates upgrading the very definition of the limit from what we saw in first year calculus.
****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
►Full Multivariable Calculus Playlist: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
****************************************************
Other Course Playlists:
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
***************************************************
► Want to learn math effectively? Check out my "Learning Math" Series:
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Want some cool math? Check out my "Cool Math" Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
*****************************************************
►Follow me on Twitter: http://twitter.com/treforbazett
*****************************************************
This video was created by Dr. Trefor Bazett.
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
Видео Limits are...weird...for multi-variable functions | Limits along paths канала Dr. Trefor Bazett
****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
►Full Multivariable Calculus Playlist: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
****************************************************
Other Course Playlists:
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
***************************************************
► Want to learn math effectively? Check out my "Learning Math" Series:
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Want some cool math? Check out my "Cool Math" Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
*****************************************************
►Follow me on Twitter: http://twitter.com/treforbazett
*****************************************************
This video was created by Dr. Trefor Bazett.
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
Видео Limits are...weird...for multi-variable functions | Limits along paths канала Dr. Trefor Bazett
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
Computing Multivariable Limits AlgebraicallyVisualizing Multi-variable Functions with Contour PlotsWhat are derivatives in 3D? Intro to Partial DerivativesThe Multi-Variable Chain Rule: Derivatives of CompositionsCalculus 3 Lecture 13.2: Limits and Continuity of Multivariable Functions (with Squeeze Th.)Directional Derivatives | What's the slope in any direction?What is a LINE INTEGRAL? // Big Idea, Derivation & FormulaHow to find the TANGENT PLANE | Linear approximation of multi-variable functionsCurves, Parameterizations, and the Arclength ParameterizationLimits of Multivariable Functions - Calculus 3Lagrange Multipliers | Geometric Meaning & Full ExampleCalculus 3 Lecture 13.1: Intro to Multivariable Functions (Domain, Sketching, Level Curves)Multivariable maxima and minimaChange the order of integration to solve tricky integralsThe Gaussian Integral // Solved Using Polar Coordinatesprecise definition of the limit for multivariable functions (KristaKingMath)What are the big ideas of Multivariable Calculus?? Full Course IntroHow long is a curve?? The Arclength Formula in 3D