ap calculus bc tuesday, 25 august 2015 objective tsw (1) estimate a limit using a numerical and...
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AP Calculus BCTuesday, 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
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TheStudentWill
Things to Remember in Calculus1. 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.
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
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
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. sin2 u
b. cos2 u
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Chapter 2Limits
7Copyright © 2014 Pearson Education, Inc.
Sec. 2.2Definitions of Limits
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.
limx c
f x L
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Copyright © 2014 Pearson Education, Inc. 11
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Sec. 2.2: Definitions of Limits
An Introduction to Limits
Ex: 3 8
, 22
xf x x
x
x 1.9 1.99 1.999 2 2.001 2.01 2.1
f (x)
2
12
2
12
11.41 11.94 11.994 undefined 12.006 12.06 12.61
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Sec. 2.2: Definitions of Limits
An Introduction to Limits
Ex:
3
?m ?l ?ix
f x
1, 3
6, 3
xf x
x
3
1limx
f x
Sec. 2.2: Definitions of Limits
An Introduction to Limits
Ex:
0
2 1 1limx
x
x1
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.
1
1lim
1x
x
x DNE
An Introduction to Limits
Ex:
It would appear that the answer is – but this limit DNE because – is not a unique number.
20
1limx x
Sec. 2.2: Definitions of Limits
DNE
An Introduction to Limits
Ex:
0
1lim sinx x
Sec. 2.2: Definitions of Limits
DNE
ZOOM IN ZOOM IN ZOOM IN
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. <Upper left corner of page>
NamePeriodAssignment