Скачать с ютуб This is the Epsilon Delta Definition of Continuity | Real Analysis в хорошем качестве

This is the Epsilon Delta Definition of Continuity | Real Analysis

The epsilon delta definition of continuity is the end of our quest for a rigorous definition of continuity. All quirks of continuity we have seen are consistent with this definition which mostly comes from the definition of a functional limit. A function f is continuous at a point c if for all epsilon greater than 0, there exists delta greater than 0 so |x-c| less than delta implies |f(x)-f(c)| less than epsilon. In this real analysis lecture we introduce this definition, equivalent definitions, properties of continuity, and a basic epsilon delta proof. #realanalysis Definition of a Functional Limit:    • Epsilon-Delta Definition of Functiona...   Proof sqrt(x) is Continuous:    • Proof: sqrt(x) is Continuous using Ep...   Sequence Definition of Continuity: (coming soon) Proving the Basic Continuity Laws: (coming soon) 1:01 Definition 3:25 Why |x-c| isn't Required to be Positive 4:12 When c is not a Limit Point 5:37 Equivalent Definitions of Continuity 7:07 Sequential Characterization of Continuity 8:19 Proving f(x)=x is Continuous using Epsilon Delta Definition of Continuity 9:56 Basic Continuity Laws 11:13 Practice Exercise: Prove sqrt(x) is Continuous Proof f(x)=x is Continuous using Epsilon-Delta Definition:    • Proof: f(x) = x is Continuous using E...   Proof |x| is Continuous using Epsilon-Delta Definition:    • Proof: f(x) = |x| is Continuous using...   Proof e^x is Continuous using Epsilon-Delta Definition:    • Proof: e^x is Continuous using Epsilo...   Proof sin(x) is Continuous using Epsilon-Delta Definition:    • Proof f(x)=sin(x) is Continuous using...   Real Analysis Course:    • Real Analysis   Real Analysis exercises:    • Real Analysis Exercises   ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Loke Tan, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon! Outro music is mine. You cannot find it anywhere, for now. Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020