AP Calculus BC
Wednesday, 09 September 2015
• OBJECTIVE TSW review for Friday’s test covering
chapter 2.
• TO RECEIVE A DROP DAILY GRADE ON
FRIDAY
– Wear a (preferably) JVHS shirt of some kind.
AP Calculus BC
Thursday, 10 September 2015
• OBJECTIVE TSW review for tomorrow’s test covering
chapter 2.
• TO RECEIVE A DROP DAILY GRADE ON
FRIDAY
– Wear a (preferably) JVHS shirt of some kind.
WS Limits and Continuity
1) a) f c  must be defined
b)
c)
lim f  x  must exist
x c
lim f  x  must equal f c 
x c
2) x  1 : asymptote, nonremovable
x  2 : gap, nonremovable
x  3 : hole, removable

3) i) f 1  is defined f 1   3
ii)
lim f  x   2 
x 1


lim f  x   2
x  1
so lim f  x  exists
x 1
iii)
lim f  x   f 1 
x 1
f  x  is not continuous @ x  1
WS Limits and Continuity
f 3 is defined f 3  2 
4) i)
ii)
lim f  x   2 

x 3
lim f  x   2
x  3
so lim f  x  exists
x 3
iii)
lim f  x   f 3
x 3
f  x  is continuous @ x  3

1
1

  
x  2 x  2
0

1
5)

lim
DNE

 x 2 x 2
1
1
l im



 x 2
x 2

0
lim
WS Limits and Continuity
x 5
lim
x  4
2
x  4
6)
x 5
lim
x  4
7)
2
x  4
1

  
0


1
 
  lim
 x 4 x 2
1

  


0


1
8
8)  
9)  
11)
10) DNE
lim f  x     VA: x  3

x 3
12)
lim f  x     VA: x  0
x  0
AP Calculus BC – Chapter 2 Test
Topics

Evaluate limits



From a graph (including left- and right-sided
limits
By using a table
Algebraically

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 2 Test
Topics

Evaluate limits (continued)


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 2 Test
Topics

Evaluate limits (continued)

Use the ε-δ definition to find δ for a given ε.
AP Calculus BC – Chapter 2 Test
Topics
Continuity.


Know and use the Definition of Continuity:
1. f  c  is defined;
f  x  exists (explicitly state this);
2. xlim
c

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 2 Test
Topics
Continuity (continued)

Know which functions are always continuous and
their domains.





Polynomial functions
Rational functions
Radical functions
Trigonometric functions
AP Calculus BC – Chapter 2 Test
Topics
Continuity (continued)

Algebraically determine points of discontinuity.



Removable and nonremovable.
Gaps, holes, asymptotes
Use and apply the Intermediate Value Theorem.

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 2 Test
Topics
Trigonometry

Values of all six trig functions at each special
angle of the unit circle.
Double-angle formulas for sine and cosine.
Prove identities.




Do not use identities to prove identies!
AP Calculus BC – Chapter 2 Test
Topics
What to study:


Your Notes

PowerPoints (they will be updated)



www.pigsflyguy.com
Assignments
Worksheets
AP Calculus BC – Chapter 2 Test
Topics

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!

Questions?