My ultimate introduction to the epsilon-delta definition of limits in calculus! The epsilon-delta definition of a limit is commonly considered the hardest topic in Calculus 1 (it's also the important part at the beginning of real analysis). The best way to understand this precise definition of a limit is to actually use an actual value for epsilon first, then solve for the corresponding delta. When writing epsilon-delta proofs for limits, be sure to set it up: given, choose, suppose, and check! εN definition (finite limit at infinity): 👉 https://www.youtube.com/watch?v=9JMFLzHtljA Check out more examples of proving limits with the εδ definition: linear, square root, and quadratic 👉 https://www.youtube.com/watch?v=yC8Y50H6kw8 1/x and x^3 👉 https://www.youtube.com/watch?v=7VSG9G6EXrU "a taste of real analysis" 👉 https://www.youtube.com/watch?v=2xmKUBgWk78 0:00 the εδ definition of a limit is the hardest topic in calculus 1 1:34 limit of sqrt(2x+1) as x approaches 4 4:14 if epsilon is 0.2, how to find the biggest delta 10:27 writing the εδ proof Get an epsilon-delta hoodie: 👉 https://blackpenredpen.creator-spring.com/listing/the-defintion Use "WELCOME10" for 10% off --------------------------------------------------------------------------------------------------- **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 Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh --------------------------------------------------------------------------------------------------- 💪 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