Description
11 1
2.3: Functions & Mathematical Models Polynomial Functions: punand function of carcen 10). axta xn't taxta x'ta wroce nisa positive cheer Due ce concos
(coned constrients 4x  3x2+x+2 (degree of 3) 275_3/2x2+4 (coefficients can be any number
(x2  4) 3 (dearce is 6 3x2  4xt to 
35 not a polynomal
Soup
StudySoup
2x31x2 + 4x 

• Domnuin of polynomial functions:
anos
• Polynomial functions of degree : loco fuoco
SCD= 34 If you want to learn more check out What does thermal energy depend on?
Study Soup
• Polynomial Bunctions of degree
Study Soup
StudySoup
Studys
6.346 & 8. Do these equations define vas a linear function of 1? If so, write it in the slopeintercept formi. Don't forget about the age old question of What is it called when you have multiple partners in a relationship?
StudySoup
3
6y +7=0
StudySoup
64+]=3x  by 37 = 4 = 1/2x+71 If you want to learn more check out What are the vertebrae in the neck region called?
Stud
2 + 4y=0 Tot locar 2x112t4yo
(
x74 07 (ou n
ot
TS
• Domain of national functions: We also discuss several other topics like Do multicellular bacteria exist?
StudySoup
Study Soup
batzę = (J
Rational Functions:Gost of 2 paurants in denominat
@ Study
Sour
Study Soup
nou od soudai= 22 +9  =
OH+2)+ch) 72 = OL+27+zCZ7Z/£ = (2)
@
w
bile telephones 2 hours after starting work?
worker
g
string work during the morning shift. Al whitral dos the phone per hour those
c=+ (#5150) OI +29+
=
v.
l d If you want to learn more check out What are the three areas in semiotics?
Delphi Eletronic I
26: Antilicjancy study showed that the NETHER Workort
Study Soup
+X=
3
htZzX=k ztx =bt (Z\ = hh rixx) W=14h
972  eh 9+Z 1  = H a+x) 1 = (x)
I
"E=T
Economile Models
Study sou
• Revenue function RLX) 
D
r. GCO SAX
Pue per un
RDS
.
avso
dinos
91,316: A If you want to learn more check out What are the different strong acids?
m e turer huis monthly fixed out of $100.000 mod a production cost of $14 for each unit produced. The products for $20 per unit.
Study Soup
(a) What is the cost function?
CO) = 14x + 100,000
Study Soup
Study Soup
StudySoup
(b) What is the revent function?
RC = P.X = 20x
@studySoup
StudySoup
udy
(
Study Soup
Study
(c) What is the profit function? P(x) = R(x)  CEx) = 20
 20% (14x+100,000)
ELX  100,000 (d) Compute the profit (or loss) corresponding to production levels of 12,000 and 20,000 units. (12,000)=L(12,000) 100,000
72.000100000 = 28,000 P(20,000) = (20,000) 100 = $ 28,000 loss
= 120,000 100,000 = 20,000 $20,000 Profit
OI=XZ O=0126
StudySoup
(oz+x) (01X 2) = CO2 + x)0102 + x2 =
100201 x Oht zx 2 = 0 Oioh of ooh
002  YO&+ 2 X 2 = o(ou os Zsos +9.2= 02X&t zX2 0 = 0
OZ+ Ol+ (92) 10 = OZ EXST 7*70 = Oh O2+(5]Z+CS)10d 02+x2 + 2X2.0= Ohtx O2 + x2+2x10= Onix  7X10
Study Soup
StudySoup
X=5
the equilibrium quantity and price.
spectively, where p in mind in dollins F
nd in umiin of hundred. Find
dy Soup
que suced
• Market equilibrium Dune
demanded =
Shu
dy Soul
SIN ', pordhesht u
Yon 2000 VOTES
1944 (33= pumj Ading. 670 P0033 photos
O
SW
BANG
Ở THỊ HẠ THINHHAT +
फारिस सपा सरकार रामपाको मायामा पर शक मगर
Stuc Soup
x OT
कमाए
HASIRTH E पा
Study Soup
=12x
Sour
studySoup
vvsarilocoo212102/1002005
cool10110050bbbb
Study Sour
2000
0 

(O) = (03
।
000

(2)=(27)
06 1)  (03
varila
2 = (x)} wy
Study
lim
f(x)=3
y =
)
f(2)=4
StudySoup
StudySoup
@
Where does a function Oil to have a limit?
StudySoup
studySoup
StudySoup
t wil
tou Sop= (
ts
>3+
Study Soup
Study Soup
Stud
EZ 1
Inat will
lim
3x  3(2) = 60
soudySoup
StudySoup
2.4.38:Find lim
+2 =
5(2)+2 =
1+z =
8
= 2
Study Soup
(
Stud
Indeterminate Form
Study Soup
2.4#52. Find ding 24* =2603(0)
0
= lim 2x3
=2(o)3=3
x=3 = lim x+2 = 312=5
{x
(2+x) (EX)
(3) Stud
hex "17=2+2=2+ h = 2+1 wil
hox
hex
StudySoup
(2+ + 2) Chat
Study Soup
Study Soup
09X  X wixz
(2+x)(+)
@ Study
2.4#60: Find lim –
1
heh
dnosapnas (
@studySoup
@studySoup
Studysou
D. NE
Sour
2= +=
849pm #2
1722=
5 = ty
z C2)
Zex
2+x
(2x) w
Cz+
(2x) = SP (9+b79b) = (9)
StudySoup
NO o
Study Soup
col001
Xoby
50
0.5 (100)
0.56x)
lim
(b) Evaluate lim C(r) and interpret your result.
StudySoup
9
Sb00!
Solop van
SYONO VOC
Sb= g Lhobl s'o= (56)
SIDOR Oligh=gh =
obool obs.0=Cob)
Colors
OS  00
c(50)=0.5(50).
SSHOV SOU
lcom
XSX =
HO SOU
Study Sour
Study Soup
Note: lim
t
o
Study SOUT
* as x
gets bigger & gets smaller
lim 2 = 0
lim t=0
x++
@studySoup
Study
Technique for evaluate the limitat infinity of a rational function:
divide numerator and denominator by xn whore nis the degree of the denominator
2.4#78: Find lim =
100 2.1
stud
+1
+1+1
Study Soup
2.1#78: Find lim 2++= m (4x 3x2+D
= lim 43 1/2 + 1/4 00 Lt) (2x + x3 + x2+x+1) X3 (2+\/x+'/x+2+x!
SEU
= lim
o=0
 en walls
be
StudySoup
4x11x
telo o
lim
4x=0
3x3 + x2 +
3 + x + x2
COS
@ when numador & beraninator are the Sorre, you will get a ratio of the Coefficient
You should be able to
StudySoup
• Evaluate limits using graphs.
• Use alegra to evaluate a limit with the indeterminate form.
Study Soup
Evalunge limits at infinity using graphs and using algelorat.
HOMEWORK, Section 2.4: 113 every other odd, 17, 2331 every other odd, 49, 53, 57, 59, 63, 65, 7385 odd
24X
Stud:
StudySoup
Study Soup
Study Soup
Cornombors slightly smaller than a) Tas x approaches a from the left

7=(x) 3 wil
Study Soup
)
(
c
) pas
• 7=(ns will
E = (35
Study Soup
&= (nt win
StudySoup
StudySoup
xSO DDE
tudy Soup
=SHOZ ON
Continuous functions:
(a) Study Soup
1=1+0=14_
OCX
3 E422
Konas
EL 14)
04X INO= 7 wy
+0FX
@
15
functions except where ocrominator iso .ONS
rational  polur
Stud
anOSA
(
Study Soup
X=(
varung hita
f(x)=5.
dnosápris
fonction Constant Things that are continuous everywhere:
Study Soup
StudySoup
i nzuri = (175 sa
7+(172 =
tax un= (y wcz
9=(h+(172) = 0
OD S: SOT
To 40 na
S IJ  co hong 3590)
(f(x) = o) on a certian interval.
has a root
con
Why do we care most ofte ud to Show took a
93
75
90 90
O NG OO
Intermediate Value Theorem:OND IS S
Study Soup
16=22=(2x) wn
= (2) 5
(2x)(2+x)
dnosapnis
Study Soup
+
2+  aX
= 36K
un = (y wi= (2) =
Sod
(D11
2016)
Study som
=X\ = X
o S
VO
StudySoup
(
T) OCTO)
O= (1x)(1+x)
Study Soul
01 = (122+8
1=4
[82]
spucoes
&
Z
]
[33
SUO SOUD
dy Soup
= 10ft/sec
188
(3,18)
=
StudySoup
Study Sour
(2709]} = sobrass+2
average webcity betw.
42
Zl=hts = (272 +9 =42+
z [hz]
Study Sol
2+2'2 utx
(27)Chahya Rooney
21= 2das
© 22 =
925 =
Owen vochty = doce
DOCH Z
Studyson
2.0 The Derivative
D 9N40 volouhodou John
hu=h4078994  COZ003
2017  COZ=114
(!) 2  zhlt LS= hinn  "Z = h
001 = (N/
100L + 201 +
9L= (oo)01= Loot @)014206) SL=(077
pocitoto2+ 90
dy Soup
StudySoup
(b) Use the Intermodinte Value Theorem la conclude that the oxygen content of the pond
must have been at a level of 80% at some time. Colo) Where is t2 +204+10o=0?
SO
01276o=(01+7) (01+7)
Shady Soup
f(t) is continuous on (0,10) because it is continuous everywhere except x=10 By N.T, the level must have been so lo at some time between ott
To=t (c) At what time(s) is the oxygen content at the 80% level?
Stud
[42+8=
= 8h+ 2h2
8=6.2= 2(2) = (2) 7
A 48+8=
Study Soup
(87 (242+48
(24+ 42+42+ h) 2 = (4+2)(4+2)2 =
(472)2 = (4+2)
Study Soup
(297(4+2) 
on the interval 2,2+HT
What is the average rate of change for our Wunction () = 2
Judysc
studySoup
.
d
Tech decor foo
Average Rate of Change New
SV SOU
b=148 =(50)2+8
go=4 [972]
spuogos
Z= 9
Z
(2) (92]) SZ=77 =7 07 TA 'JAD
9=(7) 52 = 269 27Z = (52)
the population F= 0. The graph of a gives the population dolajimlar buncitori culture of time after a portion of Elencide was introduced into the population = 0. 1 Which population is decreasing faster 7 B b. Which population is decreasing fastar 7 A
StudySoup
C. Which bactericide is more effective in reducing the
population of bacteria in the short run? In the long run?  черя, я е, че
StudySoup
Study Soup
Notation for the derivatives
f(x) = 2x2
f'(x) = 4x
0.4=2x2
41 =44
dy = 4x
StudySoup
xh = 70
tudy Soup
Stud
xh= (2+2)
@ Stud
StudySoup
Study Soup
V SOUD
= 23  (4t 2) 7
1748=(012+8=42+8
way
What is the instantaneous rite of change for our function f(1) = 21 at I=2?
VO
son of the live traccent to f ct x.
This is the
(44)
at Six to open op
. Skol DeckOC.
u
Instantaneous Rate of Change: Tercho
SOU
ful sec
= 8.002
L= (275000 25 100 0=4
10=4 sozy
 (10ozge
Cutzo
K= 2
seconds
(*) 7
(44) J
average velocity
1
272 = (7) J
/e/