Скачать или смотреть Calculus I – Lecture 10: Continuity, Types of Discontinuities & Composition

In this lecture, we develop the full theory of continuity in Calculus I.

Topics covered:

Definition of continuity at a point

Graphical meaning of continuity

Types of discontinuities: removable, jump, and infinite

Classifying discontinuities through examples

Algebra of continuous functions

Continuity of compositions

The Composition Limit Theorem

One-sided continuity

Continuity on open and closed intervals

Applications involving square-root and semicircle functions

Several worked examples illustrate how to determine and classify discontinuities and how to verify continuity on intervals.

Instructor: Prof. Shadi Shaqaqha
Department of Mathematics – Yarmouk University

شرح شامل لمفهوم الاستمرارية وأنواع عدم الاستمرارية مع أمثلة تفصيلية وتطبيقات على تركيب الدوال.

00:00 Definition of Continuity at a Point
01:59 Types of Discontinuities (Overview)
17:12 Algebra of Continuous Functions
33:42 One-Sided Continuity