MATH 242: Analysis 1 (McGill Final)

Currently Playing: x^3 is Continuous but not Uniformly Continuous (Sequential Criterion) | Real Analysis Exercises

Support the production of this course by joining Wrath of Math to access all my Real Analysis videos plus lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out my math fashion brand! https://mathshion.com/ Real Analysis course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook! https://amzn.to/4lNpyNN Business Inquiries: wrathofmathlessons@gmail.com We prove that x^3, although continuous on the reals, is not uniformly continuous. We prove this using the sequential criterion for a function failing to be uniformly continuous and then prove that x^3 is in fact uniformly continuous on any bounded subset of the reals. #realanalysis Uniform Continuity: https://youtu.be/MmxtJwr3Kws Sequential Criterion for Lack of Uniform Continuity Proof: https://youtu.be/L9XZc9m4yXg Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 0:34 x^3 is Continuous 3:07 x^3 isn't Uniformly Continuous 5:44 Uniformly Continuous on Bounded Subset 11:41 Conclusion