University Business Math Limits, Derivatives and Marginal Analysis — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 6 definitions and 7 theorems, 6 worked examples, 3 diagrams, in 15 printable pages. This page lists what the notes cover. The notes themselves come with the University Business Math bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Limits, Derivatives and Marginal Analysis — what the notes cover
7 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.
Limits from graphs and by algebra
- Definition — Limit of a function at a number
- Theorem — Finding a limit by algebra
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Infinite limits, limits at infinity and asymptotes
- Definition — Vertical and horizontal asymptotes
- Theorem — Limits at infinity of a rational function
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Continuity and sign charts
- Definition — Continuity at a number
- Theorem — The sign of a continuous function
Also in this section: 1 worked example, 1 note on method and common errors.
Rates of change and the derivative
- Definition — Average rate of change
- Definition — The derivative at a number
- Theorem — Where a derivative fails to exist
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
The power, sum and constant multiple rules
- Theorem — The basic differentiation rules
- Theorem — The tangent line at a point
Also in this section: 1 worked example, 1 note on method and common errors.
Marginal cost, revenue and profit
- Definition — Marginal cost, revenue and profit
- Theorem — Marginal revenue against marginal cost
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Business Math Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Limits, Derivatives and Marginal Analysis practice worksheet is free and stays free.
Every University Business Math topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Business Math 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, Derivatives and Marginal Analysis practice worksheet About the Limits, Derivatives and Marginal Analysis unit test