AP Calculus BC Tuesday , 27 August 2013

1. The Student Will APCalculus BCTuesday, 27 August 2013 • OBJECTIVETSW (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 (wire basket) • Acknowledgement Sheet (black tray) • I will take T-Shirt orders at the beginning of class.

2. Batteries/$$$ for Batteries • Due any time between now and 20 September 2013.

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

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

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

6. Trigonometric Notes Sheet You need to have these memorized for Friday’s quiz and for the rest of the year: • Power-Reducing Formulas • sin2u • cos2u

7. Sec. 1.2: Finding Limits Graphically and Numerically

8. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex: What is the value of as x gets close to 2? Undefined ???

9. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex: 2 2 12.06 11.41 11.94 11.994 12.61 undefined 12.006 12 12

10. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex: “The limit as x approaches two of the quantity x cubed minus 8 divided by the quantity x minus 2 is 12” “The limit as x approaches two of f(x) is 12”

11. Sec. 1.2: Finding Limits Graphically and Numerically • 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.

12. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex:

13. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex: 1

14. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex: In order for a limit to exist, it must approach a single number Lfrom both sides. DNE

15. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex: It would appear that the answer is –but this limit DNE because – is not a unique number. DNE

16. Sec. 1.2: Finding Limits Graphically and Numerically • An Introduction to Limits Ex: DNE ZOOM IN ZOOM IN ZOOM IN

17. Sec. 1.2: Finding Limits Graphically and Numerically • A Formal Definition of Limit - Definition Let f be a function defined on an open interval containing c (except possibly at c) and let L be a . The statement means that for each  > 0,  a  > 0  if “There exists” Epsilon Delta A real number “Such That”

18. Sec. 1.2: Finding Limits Graphically and Numerically • A Formal Definition of Limit - Definition

19. Sec. 1.2: Finding Limits Graphically and Numerically • A Formal Definition of Limit Ex: Given that Find  such that whenever

20. Sec. 1.2: Finding Limits Graphically and Numerically • A Formal Definition of Limit Ex: Given that Find  such that whenever