AP Calculus AB · Unit 1
Limits and Continuity
In short
Unit 1: Limits and Continuity in AP Calculus AB covers 15 topics: Introducing Calculus: Can Change Occur at an Instant?, Defining Limits and Using Limit Notation, Estimating Limit Values from Graphs, Estimating Limit Values from Tables and 11 more. Open each one for what you need to know, a self-check list and how it is tested on the exam.
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What is in Unit 1: Limits and Continuity?
Unit 1: Limits and Continuity
1.1 Introducing Calculus: Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
- I can identify when a limit might not exist for some functions at particular values of x, such as when the function is unbounded, oscillating, or when the left and right limits are not equal.
1.4 Estimating Limit Values from Tables
- I can use numerical information (such as tables of values) to estimate limits.
1.5 Determining Limits Using Algebraic Properties of Limits
- I can determine one-sided limits analytically or graphically.
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
1.8 Determining Limits Using the Squeeze Theorem
- I can use definitions, theorems, and properties to justify claims about limits.
- I can determine the limits of functions using the squeeze theorem.
- I can find the limit of a function by applying the squeeze theorem and verifying its conditions.
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
- I can justify whether a function is continuous at a specific point using the formal definition.
- I can verify the three conditions for continuity at a point: the function value exists, the limit exists, and the limit equals the function value.
1.12 Confirming Continuity over an Interval
1.13 Removing Discontinuities
- I can remove a discontinuity by defining or redefining the value of the function at a point to equal the limit of the function as x approaches that point.
- I can make a piecewise-defined function continuous at a boundary by ensuring the expressions on both sides of the boundary and the function value at the boundary are all equal.
1.14 Connecting Infinite Limits and Vertical Asymptotes
- I can describe and explain asymptotic and unbounded behavior of functions using limits.
1.15 Connecting Limits at Infinity and Horizontal Asymptotes
- I can describe the end behavior of a function using limits at infinity.
1.16 Working with the Intermediate Value Theorem (IVT)
- I can state the conditions and conclusion of the Intermediate Value Theorem for a continuous function on a closed interval.
Limits and Continuity: common questions
What is in Unit 1: Limits and Continuity?
It covers 15 topics: 1.1 Introducing Calculus: Can Change Occur at an Instant?; 1.2 Defining Limits and Using Limit Notation; 1.3 Estimating Limit Values from Graphs; 1.4 Estimating Limit Values from Tables; 1.5 Determining Limits Using Algebraic Properties of Limits; 1.6 Determining Limits Using Algebraic Manipulation; 1.7 Selecting Procedures for Determining Limits; 1.8 Determining Limits Using the Squeeze Theorem; 1.10 Exploring Types of Discontinuities; 1.11 Defining Continuity at a Point; 1.12 Confirming Continuity over an Interval; 1.13 Removing Discontinuities; 1.14 Connecting Infinite Limits and Vertical Asymptotes; 1.15 Connecting Limits at Infinity and Horizontal Asymptotes; 1.16 Working with the Intermediate Value Theorem (IVT).
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