Proving x^2 is continuous using the epsilon delta definition

Learn more about epsilon-delta definition of a limit from Brilliant via https://brilliant.org/blackpenredpen/ . That link also gives you a 20% off discount on their premium subscription. We will prove f(x)=x^2 is continuous by using the epsilon-delta definition of a limit. Today we will see one of the hardest parts of calculus, the epsilon-delta definition of limit. More specifically, the epsilon-delta definition of continuity. When math teacher struggles with epsilon-delta: 👉 https://youtu.be/TS5snj73S1g Previous upload: https://youtu.be/bT17Q-E8Tng 0:00 easy statement vs hard statement 3:31 quick review on the epsilon-delta definition 5:14 two days later (the new part) 8:46 learn more about limits on Brilliant 9:36 ending 🛍 T-shirt in the video: https://teespring.com/mathqed 10% off with the code "TEESPRINGWELCOME10" 🔑 If you enjoy my videos, then you can click here to subscribe https://www.youtube.com/blackpenredpen?sub_confirmation=1 --------------------------------------------------------------------------------------------------- ***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do*** AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi Skorj Olafsen Riley Faison Rolf Waefler Andrew --------------------------------------------------------------------------------------------------- 💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here https://www.patreon.com/blackpenredpen Thank you, blackpenredpen