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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

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 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 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