bell work for quarter i … listed in reverse order
TRANSCRIPT
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Bell Work for Quarter I
… listed in reverse order
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Essential Question(s)September 25, 2013
How do we use vertical asymptotes, horizontal asymptotes, and holes in the graph to sketch the graph of a function?
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Vol. I No. 14BSeptember 25, 2013
3 2
5
5 41) ( )
x x xf x
x x
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Essential Question(s)September 24, 2013
How do we use vertical asymptotes, horizontal asymptotes, and holes in the graph to sketch the graph of a function?
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Vol. I No. 14BSeptember 24, 2013
31) ( )
4f x
x
1
2) ( )2
f xx
2
23) ( )
1f x
x
2
34) ( )
2f x
x
Make a sketch of each function without a calculator
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Vol. I No. 14BSeptember 24, 2013
31 ) lim
4x
ax
4
31 ) lim
4x
bx
4
31 ) lim
4x
cx
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Vol. I No. 14BSeptember 24, 2013
12 ) lim
2x
ax
2
12 ) lim
2x
bx
2
12 ) lim
2x
cx
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Vol. I No. 14BSeptember 24, 2013
2
23 ) lim
1x
ax
21
23 ) lim
1x
bx
21
23 ) lim
1x
cx
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Vol. I No. 14BSeptember 24, 2013
2
34 ) lim
2x
ax
22
34 ) lim
2x
bx
22
34 ) lim
2x
cx
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Vol. I No. 14BSeptember 24, 2013
3 25 4
5) ( )4
x x xf x
x x
Make a sketch of each function with a calculator
3 2
3
5 46) ( )
16
x x xf x
x x
Identify: a) VA b) HA c) hole(s)
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Vol. I No. 14BSeptember 24, 2013
3 25 4
5) ( )4
x x xf x
x x
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Vol. I No. 14BSeptember 24, 2013
3 25 4
5) ( )4
x x xf x
x x
VA:
HA: hole(s):
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Vol. I No. 14BSeptember 24, 2013
3 2
3
5 46) ( )
16
x x xf x
x x
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Vol. I No. 14BSeptember 24, 2013
VA:
HA: hole(s):
3 2
3
5 46) ( )
16
x x xf x
x x
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Vol. I No. 14H
Section 1.5 (Infinite Limits)Page 88: 1, 3, 7, 15, 19,
28, 33, 37, 39, 41, 43, 45, 47, 49, 51, 53,
61, 64, 68
15
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Vol. I No. 15H
Section 3.5 (Limits at Infinity)Page 205: 9, 13, 15, 17, 19,
21, 23, 25, 27, 29, 31, 33,
35, 37, 39, 43, 57, 62, 63,
64, 7116
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Essential Question(s)
How do we find vertical asymptotes?
How do we find horizontal asymptotes?
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Vol. I No. 13BSeptember 23, 20132
2
2 1781) lim
3 13x
x
x
2
12 92) lim
8 3x
x
x
3
2
2 33) lim
8 5x
x
x
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As x approaches infinityLimits at Infinity
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September 23, 20132
2
2 1781) lim
3 13x
x
x
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September 23, 2013
2
12 92) lim
8 3x
x
x
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September 23, 2013
3
2
2 33) lim
8 5x
x
x
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As x approaches c
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September 23, 2013
2
31) lim
2x x
2
32) lim
2x x
2
33) lim
2x x
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September 23, 2013
2
31) lim
2x x
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September 23, 2013
2
32) lim
2x x
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September 23, 2013
2
33) lim
2x x
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September 23, 20132
22
2 84) lim
4x
x x
x
2
1
35) lim
1x
x x
x
2
1
36) lim
1x
x x
x
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Below is the graph of j(x) No. 1. 2B List as many facts about j(x) as you can.
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September 19, 20132
2
2 1781) lim
3 13x
x
x
2
12 92) lim
8 3x
x
x
3
2
2 33) lim
8 5x
x
x
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As x approaches infinity
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September 19, 20132
2
2 1781) lim
3 13x
x
x
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September 19, 2013
2
12 92) lim
8 3x
x
x
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September 19, 2013
3
2
2 33) lim
8 5x
x
x
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As x approaches c
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September 19, 2013
2
31) lim
2x x
2
32) lim
2x x
2
33) lim
2x x
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September 19, 2013
2
31) lim
2x x
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September 19, 2013
2
32) lim
2x x
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September 19, 2013
2
33) lim
2x x
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September 19, 20132
22
2 84) lim
4x
x x
x
2
1
35) lim
1x
x x
x
2
1
36) lim
1x
x x
x
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September 19, 20132
22
2 84) lim
4x
x x
x
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September 19, 2013
2
1
35) lim
1x
x x
x
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September 19, 20132
1
36) lim
1x
x x
x
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Need to Know for Test• Find limit as x approaches a value• Find left limit• Find right limit• Find points of discontinuity• Find Vertical Asymptotes• Find Horizontal Asymptotes• Find when a function is continuous• Function Analysis
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• Sketch the graph of a function• Discuss a function without a graph• Discuss a function with a graph• Squeeze Theorem• Special Limits• Identify types of discontinuities–From graph–From equation
• Do calculations from graph
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• Difference betweenDNE and DNE and
Need to Know for Test
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Work
Vol. I No. 12HPage 88: 37 – 47 (odd)
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Vol. I No. 11BSeptember 18, 2013
2 2
01) lim
x
x x x
x
0
sin( ) sin2) lim
x
x x x
x
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Vol. I No. 11BSeptember 18, 2013
0
sin( ) sin2) lim
x
x x x
x
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Vol. I No. 11BSeptember 18, 2013
2 2
01) lim
h
x h x
h
0
sin( ) sin2) lim
h
x h x
h
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The Squeeze Theorem
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This theorem concerns the limit of a function that is squeezed between two other functions, each of which has the same limit at a given x-value, as shown in Figure 1.21
The Squeeze Theorem
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The Squeeze Theorem
Figure 1.21
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Squeeze Theorem is also called the Sandwich Theorem or the Pinching Theorem.
The Squeeze Theorem
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The Squeeze Theorem
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Find
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Vol. I No. 11H
Page 67: 27-35 (odd); 49 – 63 (odd); 65 – 75 (odd)
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2 3 , 0( )
1, 0
xx xf x
x x
At what point(s) is NOT continuous?( )f x
Vol. I No. 10BSeptember 17, 2013
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2 3 , 0( )
1, 0
xx xf x
x x
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Which condition fails?
( ) lim ( ) existsx c
ii f x
( ) ( ) is definedi f c
( ) lim ( ) ( )x c
iii f x f c
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( ) ( ) is definedi f c
( ) lim ( ) existsx c
ii f x
( ) lim ( ) ( )x c
iii f x f c
Which condition fails?
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( ) ( ) is definedi f c
( ) lim ( ) existsx c
ii f x
( ) lim ( ) ( )x c
iii f x f c
Which condition fails?
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Continuity (AB)1
2
3
3, 1
( ) 1, 1 2
4, 2
x x
g x x x
x x
At what point(s) is g(x) NOT continuous?
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Continuity (AB)2
2 1, 1
( ) 3 , 1 1
2 1, 1
x
x x
h x x
x x
At what point(s) is NOT continuous?( )h x
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Continuous at x = 1
Not Continuous at x = 1
Not Continuous at x = 1
Continuous at x = 1
Continuous at x = 1
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Vol. I No. 9H
Page 78: 3, 5, 7, 9, 15, 17, 18, 19, 20, 33, 39, 43, 47, 49, 51, 53, 63, 65, 67, 75, 98
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Vol. I No. 9BFind the limit
2 2 2 2cos sin cos sin
2
2lim 2 2
3x x x x
x
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EQSeptember 16, 2013
How do you show that a function is continuous at a point?
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Vol. I No. 9 (Notes)
September 16, 2013
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What is Continuity at a Point?
2(1) ( )f x x
This function iscontinuous for all values of x
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Continuous or Not?2 4
(2) ( )2
xf x
x
This function iscontinuous for all values of x except at x=2
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Continuous or Not?
2(3) ( )
2
xf x
x
This function iscontinuous for all values of x except for x = -2
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Continuous or NOT?1
(4) ( )1
f xx
This function iscontinuous for all values of x except for x = 1
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Definition of Continuity
( ) lim ( ) ( )x c
iii f x f c
A function is continuous atif all of the following conditions are true:
f x c
( ) lim ( ) existsx c
ii f x
( ) ( ) is definedi f c
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2 3 , 0( )
1, 0
xx xf x
x x
At what point(s) is NOT continuous?( )f x
Vol. I No. 10B
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2 3 , 0( )
1, 0
xx xf x
x x
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Which condition fails?
( ) lim ( ) existsx c
ii f x
( ) ( ) is definedi f c
( ) lim ( ) ( )x c
iii f x f c
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( ) ( ) is definedi f c
( ) lim ( ) existsx c
ii f x
( ) lim ( ) ( )x c
iii f x f c
Which condition fails?
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( ) ( ) is definedi f c
( ) lim ( ) existsx c
ii f x
( ) lim ( ) ( )x c
iii f x f c
Which condition fails?
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Continuity (AB)1
2
3
3, 1
( ) 1, 1 2
4, 2
x x
g x x x
x x
At what point(s) is g(x) NOT continuous?
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Continuity (AB)2
2 1, 1
( ) 3 , 1 1
2 1, 1
x
x x
h x x
x x
At what point(s) is NOT continuous?( )h x
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Vol. I No. 9H
Page 78: 3, 5, 7, 9, 15, 17, 18, 19, 20, 33, 39, 43, 47, 49, 51, 53, 63, 65, 67, 75, 98
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EQ:How do we score an AP-Style Problem?
September 13, 2013Vol. I No. 8( )
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(a) +1(b) +4(c) +4
9
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Vol. I No. 8 ( )
Page AP1 (after p. 94): 1 – 10 Work as a team of 2, 3, or 4
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EQSeptember 9, 2013
How do you find the limit …… Graphically?… Numerically?… Analytically?… Verbally?
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Vol. I No. 7B
2
lim tanx
x
Evaluate
Graphically, Numerically, Analytically,
Verbally
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EQSeptember 5-6, 2013
How do you find the limit at a given point …
… Graphically?… Numerically?… Analytically?… Verbally?
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Evaluate Graphically
23
0(1) lim
xx
20
1(2) lim
x x
0(4) lim cot
xx
0(3) lim
2 1xx
x
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Evaluate Numerically
23
0(1) lim
xx
20
1(2) lim
x x
0(4) lim cot
xx
0(3) lim
2 1xx
x
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Evaluate Analytically
23
0(1) lim
xx
20
1(2) lim
x x
0(4) lim cot
xx
0(3) lim
2 1xx
x
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EQSeptember 4, 2013
What is a limit and how do we find it?
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Evaluate
3
(1) lim 3x
x
3
(2) lim 3xx
3
3(4) lim
3x
x
x
2
3
9(3) lim
3x
x
x
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EQSeptember 3, 2013
How do we describe the behavior of functions?
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Vol. I No. 4G (AB)August 29, 2013
Complete discussion criteria 1 – 13 and 20 for the function.
Note: Bring Calculus Book Tomorrow … and every day this week
y x
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Vol. I No. 3G (AB)(August 28, 2013)
Make a careful graph of the graph of the following function on your paper.
Complete discussion criteria 1 – 13 and 20 for the function.
Note: Bring Calculus Book Tomorrow … and every day this week
2
2
4( )
1
xy f x
x
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Vol. I No. 4G (BC)(August 28, 2013)
Make a careful graph of the graph of the following function on your paper.
Complete discussion criteria 1 – 13 and 20 for the function.
Note: Bring Calculus Book Tomorrow … and every day this week
3( )y f x x x
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Vol. I No. 2G(August 27, 2013)
Make a careful graph of the graph of the following function on your paper.
(1) y x x2
(2)1
xy
x
Complete the discussion criteria for each function.
Note: Bring Calculus Book Tomorrow … and every day this week
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Vol. I No. 1G(August 26, 2013)
Make a careful graph of each of the following functions on the paper provided.
(1) y x (2) cosy x
1(3) y
x
, 0(4)
0, 0
xx
xy
x