Mastering Continuity: 21 Comprehensive Practice Problems

Mastering Continuity: 21 Comprehensive Practice ProblemsThis essential worksheet set is designed to help calculus students master the concept of continuity at a point and over an interval. Featuring 21 diverse, thoughtfully constructed problems, this resource covers all key aspects of continuity, making it perfect for homework, quizzes, classwork, or exam review.What’s Covered?Each problem requires students to analyze a function and determine its continuity at a specific $x$-value. The functions included are:Piecewise Functions: Evaluate left-hand and right-hand limits to identify Jump and Oscillating discontinuities (Problems 1, 2, 6, 7, 8).Rational Functions: Factor and simplify to identify Removable and Infinite discontinuities (Problems 3, 4, 9).Polynomial Functions: Simple evaluation for a baseline understanding of continuous functions (Problem 5).Key Features & BenefitsDiverse Problem Types: Covers all four main types of discontinuities: Removable, Jump, Infinite, and Oscillating.Skill-Building Focus: Directly targets the three-part definition of continuity (limit exists, function defined, limit equals function value).Multiple-Choice Format: The structure of the questions is ideal for quick grading and for preparing students for standardized tests.Ready-to-Use: Just print and teach! This is a zero-prep resource for busy educators.Full Answer Key Included: Includes the correct classification for all 21 problems, allowing students to check their work or for easy teacher assessment.Ideal For:AP Calculus AB/BCHigh School Pre-Calculus/CalculusCollege-Level Calculus IReview and Remediation