Functions: Continuity and Derivability

Related lectures (31)

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Covers integration by change of variables and the derivation in chain rule.

Covers the bisection method proposition and its demonstration for finding roots.

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Explains how a function reaches its maximum and minimum values.

Explores the continuity of elementary functions and the properties of continuous functions on closed intervals.

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Covers Rolle's Theorem and the Mean Value Theorem, demonstrating their applications through examples.

Demonstrates the practical importance of the fundamental theorem of calculus through a detailed example.

Explores the Fundamental Theorem of Analysis for continuous functions on closed intervals, illustrated with examples like integrating cos(x).

Covers the Intermediate Value Theorem, uniform continuity, Lipschitz functions, and the properties of continuous functions.