Continuous Functions Explained: Polynomials, Rationals & Compositions скачать в хорошем качестве

Continuous Functions Explained: Polynomials, Rationals & Compositions

How do you instantly know if a function is continuous—and if not, where it breaks? This video reveals the hierarchy of continuous functions: why polynomials are "bulletproof," how to classify discontinuities in rational functions as holes or asymptotes using factoring, and why compositions of continuous functions inherit continuity. Key concepts covered: • Polynomials are continuous everywhere—direct substitution always works for limits • Rational functions break only where denominators equal zero • Factoring technique: canceling factors create holes, non-canceling factors create asymptotes • Proving absolute value is continuous using piecewise analysis • Composition theorem: pull continuous functions outside limits • Inverse functions inherit continuity from their original functions 📚 ORIGINAL SOURCE This video distills concepts from calculus education materials. Original:    • Calculus 1 Lecture 1.4:  Continuity of Fun...   Full credit to the original creator for the foundational content. 📺 About Lecture Distilled Long lectures. Short videos. Core insights. We transform lengthy academic lectures into focused concept videos that respect your time while delivering the essential mathematics. GitHub: https://github.com/Augustinus12835/au... #Calculus #Continuity #Polynomials #RationalFunctions #Limits #MathEducation #CalculusTutorial #Discontinuities