Lecture 39 | Discontinuities of monotonic functions on R & its left and right limits | Tamil
Definition of monotonically increasing and decreasing functions on R with examples. Existence of left and right limits of monotonic functions at every point. Monotonic functions have no discontinuities of the second kind. Let f be a monotonic function. Then the set of points at which f is discontinuous is at most countable. ================================================ Reference book: Walter Rudin, Principles of Mathematical Analysis (Third edition). For PG students studying "Analysis I". Especially for M.Sc. Mathematics (First semester) students under Manonmaniam Sundaranar University (M S University), Tirunelveli. Useful for SET/NET/GATE/other competitive examinations.
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![(M.sc-Ⅰ)If f is monotonic on [a,b] and α is cont. on [a,b] then f∈R(α)](https://i.ytimg.com/vi/naWUJBFofZs/hqdefault.jpg?sqp=-oaymwEnCNACELwBSFryq4qpAxkIARUAAAAAGAElAADIQj0AgKJDeAG4AvMY&rs=AOn4CLAUN76uD43N7BMiIVrr7oxxZFhO7Q&usqp=CCY)
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