Real Analysis Exam 2 Review Problems and Solutions скачать в хорошем качестве

Real Analysis Exam 2 Review Problems and Solutions

Main Real Analysis topics: 1) limit of a function, 2) continuity, 3) Intermediate Value Theorem, 4) Extreme Value Theorem, 5) uniform continuity, 6) differentiability, 7) Mean Value Theorem, 8) basics of Riemann integrability. https://amzn.to/3GgFjcc ("Real Analysis", by Russell Gordon) 🔴 Real Analysis Course Playlist:    • Introduction to Real Analysis Course Lectures   🔴 Abstract Algebra Course Playlist:    • Abstract (Modern) Algebra Course Lectures   🔴 Complex Analysis Course Playlist:    • Introduction to Complex Analysis Course Le...   #realanalysis #realanalysisreview #realanalysisexam Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ (0:00) Introduction (0:21) Limit of a function (epsilon delta definition) (4:52) Continuity at a point (epsilon delta definition) (7:17) Riemann integrable definition (13:12) Intermediate Value Theorem (15:33) Extreme Value Theorem (17:52) Uniform continuity on an interval (20:46) Uniform Continuity Theorem (22:11) Mean Value Theorem (25:46) Definition of the derivative calculation (f(x)=x^3 has f'(x)=3x^2) (30:11) Chain Rule calculation (32:10) Set of discontinuities of a monotone function (33:41) Monotonicity and derivatives (35:14) Riemann integrability and boundedness (37:33) Riemann integrability, continuity, and monotonicity (38:25) Intermediate value property of derivatives (even when they are not continuous) (41:37) Global extreme values calculation (find critical points and compare function values including at the endpoints of the closed and bounded interval [a,b]) (47:38) epsilon/delta proof of limit of a quadratic function (56:33) Prove part of the Extreme Value Theorem (a continuous function on a compact set attains its global minimum value). The Bolzano-Weierstrass Theorem is needed for the proof. (1:04:27) Prove (1+x)^(1/5) is less than 1+x/5 when x is positive (Mean Value Theorem required) (1:08:56) Prove f is uniformly continuous on R when its derivative is bounded on R (1:12:59) Prove a constant function is Riemann integrable (definition of Riemann integrability required) AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.