Week in Review # 9
Marcia Drost
Section 6.L,6.2,6.3
1.
2.
3.
4.
5.
6.
7.
8.
g.
10.
I
f
f
I
f
f
I
I
I
f
Fall20!4
Nov. 10,2014
tt. Sales analysis. Monthly sales of a r:. A bacteria culture is growing at the rate
particular personal computer are
W ' (t) = g.Qs\"7t grams per hour. If the
expected to decline at the rate
S'1t1 : - 21-,id
of
culture weighed 2 grams originally, what
is the weight of the culture [42[r)
computers per month, where t is time in
a. afterfhours?
months and St{ is the number of
computers sold each month. The
company plans to stop manufacturing
b. after 90
N '(t) a.l
this computer when monthly sales reach
800 computers. If monthly sales now [f =
0) are 2000 computers, find S(r). How
long will the company continue to
manufacture
this
W$)' Jo'! "o'ttd+
r tA /o &r4=o-t
, o.'l \ L-t'
de '
o.
du= t dt
,Z,q J
lc eL ' cLt
:"; ,w +e-."*U
-,t,
) ir,v6)'
#LL1
s'(1)= - ?stt/t
i3''*'
w(oj' {e" *::7"
s&)= 5 ^zst% at
S(?=-2{.tt 'r +c
s(t)= - lsTrh +c
)Co7= o*g=zo@
i-
rr. l' 2t' t+ it n,,
b)
* ti)1, !Ssno'--=,.,"
.l
i Cil* - ls tq3 + 2orrt
(t
Jw
lt- 2*t{
&.*z
rz. The rate of change of salarv for a minor
@.rb
dl,t,= Zd-x
orr"r the interval tI,161
with S[1)=1100. Find the ball player's
i"t'^--
-)^cLu--=
2
J' L'ft|.-- '{+c'
Z', ',
dv
league ballplayer is modeled by
-400+l500Ji
*
t
u=a.t
computer? Source:
CALCULUS, by Barnett, p.571,
minutes? O.l
=
e
dv
,
J-
2-t
Q41'
!
z*rsf ra
salary his 1-Otnyear.
S'=
S
il
S=
-1ootlgaox'/'
(qao+ t{oo xh )
- 4 ooy r t soc(?)
S= -r{ooyr /)o6a Xt/t
*x
*'''r,
*L
L5.
te-"
-x dx
rlLr
fui
dx
d)L=
() - - too+ laoo r C-s I lao 4<*t
L6c.0 *C; //oe
C=5OO
ji : - Ioo x 7 l,ooo y.3/z *.Soo
S (o) = -4rooo r / oao"oE/'* roa
S
, $ 28, lzZ, tl 8
-x
--
z
= J u-(-t)e
-2y
-Zx&v
= V&rl'
:-L
=
5""^
-L
z gn+C
'
*LL'-uZ +C
=
z
*tffi*
rc. [n*2,[s +t a*
&--f+r
cb--Lr
dt=
3y*a\
ntal
J,*/2.4d^*
4
S
q=y-3*zx"+2 l3J t-r- 46 dt-"
*':,:
U3f +ax
dx
1'? tL +o
a
L--rt?/' t c
ion =(x*t4*!,*
dx
t
-
ch-= d.,t
LL't? :
)L
J
nL'tz
=J(o -/2;'t')d"=
zo.
/*=
{t':)' *
T
;;
?(-nzf'/
?'
zla= Vu 4'*
t/z
(x+rz)''*c
\
Y
6Y
t)
21
-
t'Y1"
./
-.
-.
C
J4^idrfC
=
- ,i.
i'i'L(LYLI*I) +L
l-'L
\4
\.".-,.
ra. Jx(x+ z)'a*
J-L1 Y*Z
d-u -t
=,
ll
d'u-= <L/'
tL-z =
Y
{,,-rl ,i*\
=J,CI 7;W
- 2"^1 rc
u,f
" s+
't
n' 1@-a'
tJ
z:\ (xozft -J- (x + z)'
5;z
,
+C
it;u *a
dr,L + L
, ,r,ljz- t2l t\.uJ'
4r---,qt
dv
-3
4
I+a,-_l !-!?. a*
lL= y-+ 12^
dtt_--l
l-L.
t-
d4= s (xz+ Zx)d-v
; 3/"8Ut*'Y'rc
-"3
L?
25;tG)
s= /-n/x.l
-L
&=
x
dx L
e-rc
cl/,L t x
i
.>1
| x r..
/'L' !4;F;74"Y
f . ,-'/S I !-\ -t
=. \ *
\a Sat+
f - l.;e
lL? 27-t-+5dl&
+W'o
=
#
=
1x
=11 n
;1: ,
25. An object travels with a velocity
function giu"n in the fouowing figure. Find
an upper and lower estimate of the distance
traveledbytheobject,if r is measuredin
minutes and v is measured in ft/min.
t= o
f= o 5
I
23. J[ 5x."0-.'
c\ p'+^x7,
- v.L
e'
=-L\
?J
-(
Cb,
S<,clt
dx
I
l2
LO
23
t
d*
-J
2-
*;
z
-t
5
?S
Louen es[snal<,
{eo
-Y
-Ly-
"}1psr
&aa/
*.sfi.nt&e,
6
Le$t 3u,rn " Ax
A''{
{Y
ffer
85 bru+
*2 Y 4l(
zb-L=
d-u-
-) en +c'
2
*s: t '*-* *C.
3
.22l
JL=
dx
2
=
( U"{ 9, * l=* bs*J*)
l(o-{S+tZ+9-b+ 23)
= ta5
rgkut,surn' A1 (3s r !q+ bs* U* U)
r
L
= (25+ 23+zerrZ+S)
manufacturer if the marginal revenue
given by
(t-x)e"-1,
is
26. If/[x)
where .r isthe
(, - *)g,ztt-
--
ZLt ",?q
ab^LF 2(! *X) 't'{
&=
x'
n=i e*J
2
and above the x-
*J"* IL
ft"tL
a. the left.
t.
the right
AX=b:+ =!*,=L
YL3
l*
+(.
L(\u 5r * S*) =
2(4+- 16 + 2o)= r8o,
A,-zx -xz
flx]
axis from x = 0 to x = 6, using 3 rectangles
from
'
ft: J *',Y-*'(,*x)d.*
(t) t.,.
t,a* zx*y-' fr,= S
"*
&: z-2{
ot",-
d-x
v^
-[x -
area under the curve
number ofthousands ofpurses sold.
fn& , &'
=
rgs
4)z + 20, approximate the
/-
^a--l
t-(-a
?
2($. * su * 5r)
=
:
'Zltre+2a+- tqa) a ro!t,
27. How many rectangles should be used in
the previous problem so that the error is less
than L?
\S."y-SC*)l . Ar
z ISc"t-$to)l.g:qr
Lrut4rr,=
fo,o]
-Til--
=ltb-+l- co-a 1t
rt-
1z-.
-
tl a I
11hz< n'
':,._r.t
.l2l
zf,.From a study on memorizing facts, a
researcher found on average, the rate of
learning facts, N ' kJ after x hours of
studying was defined approximately by
the followins
ng values:
val
z
4
x
0
6
B
10
L2
N'fxl 30 26 22 20 1B L6 t2
Use
left and right sums over tUlgg_
to approxi mate
the area under the graph of N'(xJ
eq ual - sub-it1[e-nrals;
(L=a
-'tglL-
from x = 6 to x = L2. Calculate the
error bound.
piIin{he blanks:
,- f'
Lfgi
<-Jo
L= 2(So *
A,(,)u,.
Sg
*
/j|6
Lbl4
Ax' y9- = L
b
t,o) = z(2o+ rE+r b)
z2(s{)=to8
R'= z(5,.+ Uro*Us)= z(tz+tb+ lg)
= <16)