information :

Chapter 7 : only cover 7.1 and 7.2

( 7.4 excluded )

SupwMakeups_i.Emailmeatjohnstou@math.amass.edu

and includedocumentation as to why you

qualify for a Super makeup.

Thm

Fundamental of Calculus y -

tahrsatfandxiFad - Fa ) -

whereF'M=£#gdofhndx

Fad-Fca)=Satfad×=Fad = Fla ) + Sad Ftxdx

¥+4 Fha Tuten rate of

change ,Ffx ) ,

of Ex ,

Find En can be HARD !

nrnateof change

•

Aside

csFoIE@tIrt.oIt • period

A in anF¥IaAn.ya+r(H=TosinlTt ) period : 2T '

-

Area = + area + faredAmplitude

=lAl=D loan # G-period

.es#iiEtIkBosMnY.q+

=D

t*

> 0,

some time in the future

s ( t ) - position r ( H = ( o sin Cat )

( or U CH )

p*EE¥¥¥1,t.MN#3anr9E

change in position over

[ 0,

t* ] t.me period

exi .

Sal = Sk ) tSorct# > 0

@=Sco ) + Spread o= Sco )+0=4

Note '

. y= fix , = - × +1

Area between fix ,

± - and the * axis over

±÷i¥y.

[ 923 is �1�

f- xnax = 0 E - I )

= t ( 20 - 7t ) = 0

⇒ to or 20-77=0 or t= 2yd

t÷tIDI¥I¥E¥:t*÷mn¥*@a 27.211 ..

.

- ( -0211.

..

i) >

.

= 27.422 . ..÷

422

Note :

Fiat dtp# tut = { lntsldt

account for F 27 ,422 . - .

" I:iInl#¥*

2629

c CH - coverage at time t

C ( 0 ) = 2002

C ( 241 = Ca ) +

5o2tdH1dt-2oo2tSo248rdt-2oo2t8f2ttt@F2002t627.O

69 = 2629.069 ..

. .

Exactly. gout"

'dt EE

Fl24l*Flo)

Wwhere Ftt )=fH)=t" 2

fft ) -

what is FAI ? f 'H= ( t' 'D '=

tzt42pow_rueFTt3t3Fc-yEtHrkrtLareIinantpIIEIin.t.atsrettnE-1t42-8Ifs2FHHFcYtAYes-ste2@a627.o

oq . . |§¥jhtt=¥tY+cExact

=¥Ftc

pr.fi#adRue an

9- # widgets we Produce 49¥16 ••

¥" ⇐

ftp.go#*o⇒

profit RevenueCost

, ,

g*

9*+19Maximize Profit c) variable

⇐Pyq)=R' G) - dcq )

Erena EndT.ae/r#FEEfE

unit

aCCO) = 13,000 190

caqo )= do ) tfdlqdq0

22,55021)

= 13,000+558.0085-9+494

= 13,000 + 955043

= 2255043

147.80 c'

1 |qo)= 147.8

marginal cost

22,55043+147.80 when 9=190