Ap calculus bc tuesday 27 august 2013
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T he S tudent W ill. AP Calculus BC Tuesday , 27 August 2013. 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.

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AP Calculus BC Tuesday , 27 August 2013

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Ap calculus bc tuesday 27 august 2013

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.


Batteries for batteries

Batteries/$$$ for Batteries

  • Due any time between now and 20 September 2013.


Things to remember in calculus

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.


Trigonometric notes sheet

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


Trigonometric notes sheet1

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


Trigonometric notes sheet2

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


Sec 1 2 finding limits graphically and numerically

Sec. 1.2: Finding Limits Graphically and Numerically


Sec 1 2 finding limits graphically and numerically1

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

???


Sec 1 2 finding limits graphically and numerically2

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


Sec 1 2 finding limits graphically and numerically3

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”


Sec 1 2 finding limits graphically and numerically4

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.


Sec 1 2 finding limits graphically and numerically5

Sec. 1.2: Finding Limits Graphically and Numerically

  • An Introduction to Limits

    Ex:


Sec 1 2 finding limits graphically and numerically6

Sec. 1.2: Finding Limits Graphically and Numerically

  • An Introduction to Limits

    Ex:

1


Sec 1 2 finding limits graphically and numerically7

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


Sec 1 2 finding limits graphically and numerically8

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


Sec 1 2 finding limits graphically and numerically9

Sec. 1.2: Finding Limits Graphically and Numerically

  • An Introduction to Limits

    Ex:

DNE

ZOOM IN

ZOOM IN

ZOOM IN


Sec 1 2 finding limits graphically and numerically10

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”


Sec 1 2 finding limits graphically and numerically11

Sec. 1.2: Finding Limits Graphically and Numerically

  • A Formal Definition of Limit

    - Definition


Sec 1 2 finding limits graphically and numerically12

Sec. 1.2: Finding Limits Graphically and Numerically

  • A Formal Definition of Limit

    Ex: Given that

    Find  such that

    whenever


Sec 1 2 finding limits graphically and numerically13

Sec. 1.2: Finding Limits Graphically and Numerically

  • A Formal Definition of Limit

    Ex: Given that

    Find  such that

    whenever


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