AP Calculus AB Limits and Continuity — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 12 definitions and 6 theorems, 3 worked examples, 5 diagrams, in 16 printable pages. This page lists what the notes cover. The notes themselves come with the AP Calculus AB bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Limits and Continuity — what the notes cover
8 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Rate of change
- Definition — Average rate of change
- Definition — Instantaneous rate of change
Also in this section: 1 worked example.
What a limit is
- Definition — Limit
- Definition — One-sided limits
- Theorem — Existence of a two-sided limit
Also in this section: 1 diagram.
Finding a limit
- Theorem — The limit properties
- Definition — Indeterminate form
Also in this section: 1 worked example, 2 notes on method and common errors.
The squeeze theorem
- Theorem — The squeeze theorem
Also in this section: 1 note on method and common errors, 1 diagram.
Continuity
- Definition — Three kinds of discontinuity
- Definition — Continuity at a point
- Theorem — Continuity of the elementary functions
- Definition — Continuity on an interval
Also in this section: 1 worked example, 1 diagram.
Asymptotic behaviour
- Definition — Infinite limit
- Definition — Vertical asymptote
- Definition — Limit at infinity
- Theorem — End behaviour of a rational function
- Definition — Horizontal asymptote
Also in this section: 1 note on method and common errors, 1 diagram.
The Intermediate Value Theorem
- Theorem — Intermediate Value Theorem
Also in this section: 1 note on method and common errors, 1 diagram.
Where the notes are
The notes are one of the documents in the AP Calculus AB Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Limits and Continuity practice worksheet is free and stays free.
Every AP Calculus AB topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 8 AP Calculus AB units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Limits and Continuity practice worksheet About the Limits and Continuity unit test