1. Limits + continuity

Introduction to limits:

View + take notes from Limits at calculus-help.com

View Limits on Youtube, and search for other youtube videos on limits.

mathtv.com is an excellent resource for much of the course, giving a tv commentary on many worked examples, including in Spanish. You should view the multiple-choice questions on limits plus questions 5 onwards... look for the side menu calculus/limits. (mathtv also covers the epsalon-delta definition of limits... this goes beyond our AP Calc syllabus, but the questions are worth a look, but no more.)

Go to onlinemathlearning.com and view the formal definition of a limit, evaluating limits and 2 techniques for evaluating limits and the overview of limits.

There are numerous tutorials and demos on limits and continuity at visual calculus. You should do the questions on the definition of limits, evaluating limits symbolically, piecewise functions, horizontal asymptotes and vertical asymptotes

L'Hopital's rule is not in the syllabus, but it can be helpful in understanding limits to review it. Visual calculus has questions and solutions on L'Hopital's Rule and more questions and solutions.


Other resources + web sites:

Here is a mindmap on limits and here is a mindmap on continuity

An online limits calculator is at: numberempire.com

A Geometer's Sketchpad demo + exercise on limits can be downloaded and run locally on school laptops/computers: GSP limits

Also see: algebralab.net and sosmath.com.

Packet on limits and continuity to practice evaluating limits numerically, graphically and algebraically + continuity in terms of limits + asymptotes and limits involving infinity.

Textbook:

Limits: ch 1 pages 41 to 64 (skip 52-54).

Attempt the odd number exercises (answers in back of the book) on pages 54 to 56, and 65 to 67. The more you do...

Continuity: pages 68 to 74.

Exercises: odd numbers, pages 76 to 79.

Infinite limits: pages 80 to 84.

Exercises: odd numbers, pages 85 to 87.

Review: odd numbers, pages 88 to 89.

AP Calc questions:

1998 multiple choice # 12

1997 multiple choice # 15, 21

1993 multiple choice # 3

1988 multiple choice # 29, 41

1969 multiple choice # 6

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