MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proving all the Function Limit Laws | Real Analysis

Support the production of this course by joining Wrath of Math to access all my real analysis videos plus the lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Get the coolest math clothes in the world! 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/45kcMjq We prove the algebraic limit laws for limits of functions. To do this we use the theorem connecting functional limits to sequential limits. The limit of a constant multiple times a function, the sum of functions, the product of functions, and the quotient of functions, are all exactly what you'd expect. #realanalysis Epsilon-Delta Definition of the Limit of a Function: https://youtu.be/kVQNhAIFZYc Connecting Function Limits and Sequence Limits: https://youtu.be/7svyCaVjH6w Sequential Criterion for Divergent Limit: https://youtu.be/vGT1ohQHo5k ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu 0:00 Intro 1:34 Constant Multiple Law kf(x) 2:59 Sum of Function Limits Law f(x) + g(x) 4:13 Product of Function Limits Law f(x)g(x) 5:27 Division of Function Limits Law f(x)/g(x) 7:09 Outro