1. AP Calculus BC Tuesday, 25 August 2015 OBJECTIVE TSW (1) estimate a limit using a numerical and graphical approach; (2) learn different ways that a limit can fail to exist; and (3) study and use a formal definition of a limit. FORMS DUE (only if they are completed & signed) –Information Sheet & Acknowledgement Sheet (wire basket) The Student Will

2. Things to Remember in Calculus 1.Angle measures are always in radians, not degrees. 2.Unless directions tell otherwise, long decimals are rounded to three places (using conventional rounding or truncation). 3.Always show work – Calculus is about communicating what you know, not just whether or not you can derive a correct answer.

3. Trigonometric Notes Sheet You need to have these memorized for Friday’s quiz and for the rest of the year: 1.Definition of the Six Trig Functions (including the pictures) a.Right Triangle Definitions b.Circular Function Definitions 2.Reciprocal Identities 3.Tangent and Cotangent Identities 4.Pythagorean Identities

4. Trigonometric Notes Sheet You need to have these memorized for Friday’s quiz and for the rest of the year: 5.Unit Circle a.Special angles (in radians) b.Sines, cosines, tangents, secants, cosecants, and cotangents of each special angle 6.Double-Angle Formulas a.sin 2u b.cos 2u

5. Trigonometric Notes Sheet You need to have these memorized for Friday’s quiz and for the rest of the year: 7.Power-Reducing Formulas a.sin 2 u b.cos 2 u

6. Copyright © 2014 Pearson Education, Inc. 6 Chapter 2 Limits

7. 7 Copyright © 2014 Pearson Education, Inc. Sec. 2.2 Definitions of Limits

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9. Sec. 2.2: Definitions of Limits An Introduction to Limits (informal) Definition: Limit If f (x) becomes arbitrarily close to a single number L as x approaches c from both the left and the right, the limit as x approaches c is L.

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14. Copyright © 2014 Pearson Education, Inc. 14 Table 2.2

15. Sec. 2.2: Definitions of Limits An Introduction to Limits Ex: x1.91.991.99922.0012.012.1 f (x) 2 12 2 11.4111.9411.994 undefined 12.006 12.06 12.61

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17. Copyright © 2014 Pearson Education, Inc. 17 Figure 2.11 (a & b)

18. Copyright © 2014 Pearson Education, Inc. 18 Figure 2.12 (a & b)

19. Copyright © 2014 Pearson Education, Inc. 19 Table 2.3

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22. Sec. 2.2: Definitions of Limits An Introduction to Limits Ex:

23. Sec. 2.2: Definitions of Limits An Introduction to Limits Ex: 1

24. Sec. 2.2: Definitions of Limits An Introduction to Limits Ex: In order for a limit to exist, it must approach a single number L from both sides. DNE

25. An Introduction to Limits Ex: It would appear that the answer is –  but this limit DNE because –  is not a unique number. Sec. 2.2: Definitions of Limits DNE

26. An Introduction to Limits Ex: Sec. 2.2: Definitions of Limits DNE ZOOM IN

27. Sec. 2.2: Definitions of Limits Assignment: WS Sec. 2.2  1-4, 7, 9-11, 19, 20, 22  Put answers on a separate sheet of notebook paper. Name Period Assignment

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29. Copyright © 2014 Pearson Education, Inc. 29 Figure 14