Transcript AP Calculus BC – Chapter 1 Test Topics

AP Calculus BC
Friday, 05 September 2014
• OBJECTIVE TSW review for Monday’s test covering
sec. 1.2 – 1.5 and trigonometry.
• T-Shirt money is due by next Friday, 09/12/14.
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S – XL $8.00
– 2XL – 4XL $10.00
• ASSIGNMENTS DUE MONDAY
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Sec. 1.4
Sec. 1.5
WS Limits
WS Sec. 1.3 – 1.4
New T-Shirt Design This Year
(Front)
FALCON
CALCULUS
(Back)
“Calculus has its limits.”
- Anonymous
AP Calculus BC – Chapter 1 Test
Topics
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Evaluate limits
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From a graph (including left- and right-sided
limits
By using a table
Algebraically
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When a limit DNE because the one-sided limits are
different, state both one-sided limits and state that they
are not equal before stating the limit DNE.
AP Calculus BC – Chapter 1 Test
Topics
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Evaluate limits (continued)
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one-sided limits;
involving special trigonometric functions.
sin x
lim
1
x 0
x
1  cos x
lim
0
x0
x
AP Calculus BC – Chapter 1 Test
Topics
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Evaluate limits (continued)
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Use the ε-δ definition to find δ for a given ε.
AP Calculus BC – Chapter 1 Test
Topics
Continuity.
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Know and use the Definition of Continuity:
1. f  c  is defined;
f  x  exists (explicitly state this);
2. xlim
c
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Both one-sided limits must be stated before this can be
determined.
3. lim f  x   f  c  .
x c
 ∴ f (x) is continuous @ x = c.
AP Calculus BC – Chapter 1 Test
Topics
Continuity (continued)
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Know which functions are always continuous and
their domains.
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Polynomial functions
Rational functions
Radical functions
Trigonometric functions
AP Calculus BC – Chapter 1 Test
Topics
Continuity (continued)
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Algebraically determine points of discontinuity.
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Removable and nonremovable.
Gaps, holes, asymptotes
Use and apply the Intermediate Value Theorem.
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i.
ii.
The function is continuous;
f (a) < k < f (b).
∴, by the IVT, there exists a c in [a, b] such that
f (c) = k.
AP Calculus BC – Chapter 1 Test
Topics
Trigonometry
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Values of all six trig functions at each special
angle of the unit circle.
Double-angle formulas for sine and cosine.
Prove identities.
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Do not use identities to prove identies!
AP Calculus BC – Chapter 1 Test
Topics
What to study:
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Your Notes
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PowerPoints (they will be updated)
Assignments
Quiz 1.2-1.3 & Trig Review
WS Trig Review
WS Limits
WS Sec. 1.3 – 1.4
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AP Calculus BC – Chapter 1 Test
Topics
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The test will be part with calculator and part
without.
Remember: The key to success is to
communicate what you know, not just get a
correct answer.
Suggestion: Get together with a study group
– there is power in numbers!
Wear a Falcon shirt, preferably purple !