Calc AB · U1
Limits and Continuity
Build intuition for limits, learn to evaluate them algebraically, and understand what makes a function continuous.
Test yourself
A focused, distraction-free run through 80 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 1.1
Introducing Calculus: Can Change Occur at an Instant?
Interpreting instantaneous change as the limiting value of average rates of change
Topic 1.2
Defining Limits and Using Limit Notation
Reading, writing, and interpreting two-sided and one-sided limit notation
Topic 1.3
Estimating Limit Values from Graphs
Reading approaching values, holes, jumps, and vertical behavior from graphs
Topic 1.4
Estimating Limit Values from Tables
Using numerical evidence from values near, but not necessarily at, the input
Topic 1.5
Determining Limits Using Algebraic Properties of Limits
Applying sum, difference, product, quotient, power, and root limit laws
Topic 1.6
Determining Limits Using Algebraic Manipulation
Factoring, conjugates, expansion, and complex fractions for indeterminate forms
Topic 1.7
Selecting Procedures for Determining Limits
Choosing direct substitution, factoring, conjugates, tables, graphs, or squeeze reasoning
Topic 1.8
Determining Limits Using the Squeeze Theorem
Trapping a function between two functions with the same limiting value
Topic 1.9
Connecting Multiple Representations of Limits
Reconciling formula, graph, table, and verbal evidence about the same limit
Topic 1.10
Exploring Types of Discontinuities
Distinguishing removable, jump, infinite, and oscillatory discontinuities
Topic 1.11
Defining Continuity at a Point
Checking the three point-continuity conditions: defined value, existing limit, and equality
Topic 1.12
Confirming Continuity over an Interval
Determining intervals where standard and piecewise functions are continuous
Topic 1.13
Removing Discontinuities
Redefining point values to patch removable discontinuities when possible
Topic 1.14
Connecting Infinite Limits and Vertical Asymptotes
Using one-sided infinite limits to identify and describe vertical asymptotes
Topic 1.15
Connecting Limits at Infinity and Horizontal Asymptotes
Using end behavior to identify horizontal asymptotes and long-run function values
Topic 1.16
Working with the Intermediate Value Theorem (IVT)
Using continuity on a closed interval to guarantee values between endpoint outputs