capitulo 5 flemming resolvido calculo a 5ª edição
DESCRIPTION
Capitulo 5 Capitulo 5 1)Flemming resolvido meu rascunho de estudo os primeiros capitulo É rascunho que eu uso de estudo faltam alguns exercicios.É rascunho lembre-se disso na hora de abrir istoOs graficos podem ser feitos em qualquer programas de computador.Os que nao tem respostas aqui tem tem resolvido no stewartOs que nao tem respostas aqui tem tem resolvido no stewartTRANSCRIPT
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Capitulo 5
1
Capitulo 5
1)
( ) 16 ²f t t t
a)
2 216( ) ( ) 16 16 2b h b h b bVm b hb h b
(1)
b)
(16 2 ) /b h m s
3
0,122,1 /
0,0122,01 /
0,00122,001 /
b
hVm m s
hVm m s
hVm m s
c)
( ) 16 ²'( ) 16 2
f t t tf t t
d)
t=3s
'( ) 16 2(3) 22 /f t m s
e)
( ) 16 ²'( ) 16 2''( ) 2 / ²
f t t tf t tf t m s
2)
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Capitulo 5
2
a)
( )
'( )²
bf t ctt
bf t ct
( )4bv t c
b)
( )
'( )²
2''( )³
bf t ctt
bf t ctbf t
t
3)
3 ² ³6 3 ²6 6
x t tv t ta t
a)
2 3
3 ² ³3(4) (4) 16
x t tx m
b)
13 /
20 /
39 /
424 /
t sv m s
t sv m s
t sv m s
t sv m s
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Capitulo 5
3
c)
10 / ²
26 / ²
312 / ²
418 / ²
t sa m s
t sa m s
t sa m s
t sa m s
a=-18m/s²
4)
2102
0 0 /' 0
14,99,8 /
219,619,6 /
y v t gt
v m sy v v gtt sy mv m s
t sy mv m s
5)
2120 4( ) 2
24, 4 604
4'( )
24, 4
tw t
t
tw t
a)
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Capitulo 5
4
'( ) 4 54 /w t t g dia
b)
2 21 1(51) (50) 20 51 4 20 50 4 54,52 2
w w g
c)
'( ) 24, 4 /w t g dia
6)
4'( ) 5( 1)²
2'( ) 5,444 /
T tt
t hT t C h
7)
6
'²
' .10 / ³ ² 10 ²
cvp
cvp
c cv cmKgf cm Kgf
8)
a)
90000 2500 ²0
6
V tVt horas
b)
90000 2500(5)² 90000 2500(2)²(5) (2)( ) 17500 /2 1 3
V Vtaxa media l ht t
c)
' 5000 10000 /taxa V t l h
9)
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Capitulo 5
5
a)
( ) 4500 1550P t t
b)
'( ) 1550 /taxa P t reais ano
c)
(var , , ) '( ) 1550 /(2) (1)(var ) ( ) 1500
2 1var ( )
taxa iaçao do aluguel P t reais anoP Piaçaodoaluguel taxa media
iaçao reajusteanoporcentagemreajustetotal
d)
10)
a)(milhares/ano)
5 5'( ) 0,8 / ²1 ² 1,5 1 ²
taxa p t milhares anot
b)Só variação de pessoas
5 5( ) 20 20 0,0672 1 1 1
192 1,5833333333333333312181 1,512
taxa real milharest t
t
t
11)
3
3
13 ²1
12
x rdrdx xdrdx
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Capitulo 5
6
12)
12( ) 51'( ) 5 4,875 /
2
f t t t
f t l hx
13)
510
( ) 25².
( ) ²
25 ³ / 1 0,318(5 )²
r mh mV t tV r hArea base r
m h m mvm h h
( ) 25( ) ². 10
25 25
V t tV t r ht horas
14)
a)
3
2
2 2
31 .3
( _ _ ) 3 .
1( _ _ ) 33 3 3
V x
d xdx dddd dddV dxtaxa em relaçao aresta xdt dtdV d dtaxa em relaçao Diagonaldd
b)
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Capitulo 5
7
2
2
1 .3
1( _ _ ) 3 .3 3
3
3 18 3.2 6 3 ³ /3 3 3
dx dddt dt
dV d ddtaxa em relaçao Diagonaldt dt
d m
dV m sdt
15)
a)
1 ²3434 ³9
4 4². ²3 3
V r h
h r
V r
dV drr rdr dr
b)
4 4². 2 ². 0, 2 3,35 ³ /3 3
dV drr m sdt dt
16)Confirmar área do triangulo
a)
3 ²2
3 3 12. 3. 2,5 30 3 ² /
A x
dA dx dxx x cm sdt dt dt
b)
3
3 7,5 /
p xdp dx cm sdt dt
17)
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Capitulo 5
8
2 ² 3 1
4 3
4.(0).6 3.6 18 / min
y x xdy dx dxxdt dt dtdy unidadesdt
18)
Teremos um triangulo
80 / . 6,5 520
95 / . 4,5 427,5² ² ²
673, 2
520.80 427,5 .95122,1 /
673, 2
y km h h km
x km h h kmz x yz km
dz dx dyz x ydt dt dt
dz km hdt
19)
4 0,9
4 0,93,1 0,9
3,1 0,9
0,9 .51, 45 /
3,1
x z xx x z
x zdx dzdt dt
dx m sdt
20)
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Capitulo 5
9
3
23
13
13
3 3
1 . ²312
. ²
6
6.
1 6 6. .3
6 4 226 3
V r h
r h
Ab r
Vr
VAb
Ab VdV
Ab VdV V V
5.11(Desenhar)Arrumar todos os graficos
1)Falta colocar intervalo
a)
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Capitulo 5
10
1'( )²
1 113 2'( )
3 2 61 1² 6
6
f cc
f c
cc
b)
1'( )²
1 113 1'( )
3 1 31 1² 3
f cc
f c
c
c)
x
y
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Capitulo 5
11
'( ) 3 ²64 0'( ) 164 0
3 ² 1643
f c x
f c
x
x
d)
'( ) 3 ²8 0'( ) 42 0
3 ² 423
f c x
f c
x
x
e)(colocar em pi)
x
y
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Capitulo 5
12
'( )0 1 2'( )
22( )
2
f c senx
f c
sen c
arcsen c
f)
x
y
x
y
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Capitulo 5
13
'( ) sec ²1 1 2'( )
22sec ²( )
f c x
f c
c
g)
'( ) sec ²1 0 4'( )
42sec ²( )
2
f c x
f c
c
arcsen c
h)
x
y
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Capitulo 5
14
2
2
'( )1
0 1'( ) 11
11
12
xf cx
f c
cc
c
i)
3
3
23
1'( )3 ²1 1'( ) 11 1
1 13 ²
131
3 3
f cc
f c
c
c
c
j)
x
y
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Capitulo 5
15
'( ) 1, 0'( ) 1, 0
1 1'( ) 11 1
f c xf c x
f c
2)
3
1'( )²
0 0'( )0 0
f cc
f c
3)
'( ) 4 ³ 16'( ) 4 ³ 16 0
4 [ ² ] 00, 2, 2
f c x xf c c cc c c
c c c
4)
Ver teorema
5)
É só colocar o valor de x achado em f’(x)=0 ,em f(x),assim acharemos se é máximo ou mínimo.
a)
' 3y x
x
y
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Capitulo 5
16
b)
' 2 30 2 3
32
y xx
x
c)
' 2 2' 0
1
y xyx
x
y
x
y
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Capitulo 5
17
d)
² 2 8' 2 2' 0
1
y x xy xyx
e)
x
y
x
y
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Capitulo 5
18
3 ³' 3 ²' 0
0
y xy xyx
f)
' 3 ² 4 5y x x
g)
x
y
x
y
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Capitulo 5
19
' 4 ³ 12 ²' 0
0, 3
y x xyx x
h)
xy
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Capitulo 5
20
i) Colocar pi
j)
x
y
x
y
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Capitulo 5
21
' cos' 0
cos34
y x senxy
x senx
x
k)
' 1' 0
1ln ln1
0
x
x
x
y eye
ex
x
y
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Capitulo 5
22
l)
3
1'3 ² 9
' 00, 3, 3
xyx
yx x x
m)
x
y
x
y
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Capitulo 5
23
2
² 4'
² 4x
yx
n)
32,2
32,2
x
x
x
y
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Capitulo 5
24
o)
1, 02 , 0
xx x
6)
a)
'( ) 2f x
x
y
x
y
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Capitulo 5
25
b)
'( ) 5f x
c)
'( ) 6 6'( ) 0
1
f x xf xx
x
y
x
y
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Capitulo 5
26
d)
'( ) 3 ² 4 4'( ) 0
232
f x x xf x
x
x
x
y
x
y
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Capitulo 5
27
e)
'( ) 3 ² 7'( ) 0
73
f x xf x
x
f)
1'( ) cos2
'( ) 023
43
f x x
f x
x
x
g)
'( ) 2 ln 2'( ) 0
xf xf x
x
y
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Capitulo 5
28
h)
'( ) xf x e
x
y
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Capitulo 5
29
i)
0
'( )'( ) 0
ln lnln ln
ln ln lnln 0
1
x x
x x
f x e xef x
e xex e x xee x ex
x e
x
y
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Capitulo 5
30
j)
2² 2'( )
1'( ) 0
021
x xf xx
f xxxx
x
y
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Capitulo 5
31
k)
1'( ) 1²
'( ) 01
1
f xx
f xxx
x
y
x
y
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Capitulo 5
32
l)
'( ) cos'( ) 0
cos
4
x xf x e senx e xf x
x senx
x
7)
c)
x
y
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Capitulo 5
33
'( ) 3 6'( ) 0
12
3 22
1 132 4
f x xf x
x
f
f
d)
'( ) 3 ² 2'( ) 0
023
5 100
2 43 27
f x x xf xx
x
f
f
x
y
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Capitulo 5
34
e)
1 ²'( )1 ² ²
'( ) 01
1112
112
xf xx
f xxx
f
f
x
y
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Capitulo 5
35
f)
1, 01, 0x
x
x
y
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Capitulo 5
36
g)
'( )'( ) 0
020
(0) 1
x x
f x senhxf xe e
xf
x
y
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Capitulo 5
37
h)
'( ) sec ²f x hx
x
y
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Capitulo 5
38
i)
j)
k)
l)
8)É só derivar e achar x em f’(x)=0
E verificar quando f’(x)>0 e f’(x)<0
a)
x
y
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Capitulo 5
39
b)
c)
x
y
x
y
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Capitulo 5
40
d)
x
y
x
y
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Capitulo 5
41
e)
f)
x
y
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Capitulo 5
42
g)
x
y
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Capitulo 5
43
h)
x
y
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Capitulo 5
44
j)
x
y
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Capitulo 5
45
k)
x
y
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Capitulo 5
46
i)
x
y
x
y
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Capitulo 5
47
l)
m)
x
y
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Capitulo 5
48
9)
a)
'( ) 14 6'( ) 0
37
f x xf x
x
y
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Capitulo 5
49
b)
'( ) 4 2'( ) 0
2
f x xf xx
c)
x
y
x
y
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Capitulo 5
50
'( ) ² 6 7'( ) 0
71
f x x xf xxx
d)
'( ) ³ 5 ² 8 4'( ) 0
1
f x x x xf xx
x
y
x
y
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Capitulo 5
51
e)
26
0
tt
t
f)
x
y
x
y
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Capitulo 5
52
13'( ) 4 2
'( ) 08
f x xf xx
g)
257'( ) ( 2)
5f x x
h)
134'( ) (2 3)
3'( ) 0
32
f x x
f x
x
x
y
![Page 53: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/53.jpg)
Capitulo 5
53
i)
216 4 ²'( )
² 4'( ) 0
22
xf xx
f xxx
j)
x
y
x
y
![Page 54: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/54.jpg)
Capitulo 5
54
2 2 1 ² 2 2 ² 2 4'( )² 2 2 ² ² 2 2 ²
'( ) 0
1 5
x x x x x xf xx x x x
f x
x
k)
x
y
x
y
![Page 55: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/55.jpg)
Capitulo 5
55
'( ) 2( 2)( 1)³ 3( 2)²( 1)²'( ) 0
245
f x x x x xf xx
x
l)
12
1 12 2
² 64 5 ²'( ) 2 162 16 2 16
'( ) 00645
x x xf x x xx x
f xx
x
10)
1 1'( ) .log log² ²
'( ) 0log log
a a
a a
f x x ex x
f xx e
x e
11)
'( ) 3 ² 2
12 4 03
( 2,1)( ) 1
1 8 123
f x x axa
a
f xb
b
12)
![Page 56: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/56.jpg)
Capitulo 5
56
'( ) 6 ² 26 2 0
03
(0)(1) 2
f x ax bx ca b c
cb a
f df a b c d
13)
'( ) 2'( ) 2'( ) 0
0
20
2
f x ax bf x ax bf xa
bxa
abxa
14)
a)
''( ) 6 10''( ) 0
53
f x xf x
x
b)
''( ) 36 ² 60 24''( ) 0
213
f x x xf xx
x
c)
32''( )
4f x
x
d)
![Page 57: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/57.jpg)
Capitulo 5
57
3 3''( ) 12 18''( ) 0
23
x xf x e xef x
x
e)
2 2''( ) 2 4 [2 4 ]''( ) 0
2 2
x x x xf x e xe x e e x xf x
x
f)
3
1''( ) 21 ²
f xx
g)
h)
''( ) 2''( ) 0
tf x e sentf xx
i)
2, 1''( )
0, 1x
f xx
j)
2, 1''( )
2, 1x
f xx
15)
a)
4,4
4lim lim 0,44 1x x
x vertical
x horizontalx
x
![Page 58: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/58.jpg)
Capitulo 5
58
b)
2,3
3lim lim 0,22 1x x
x vertical
x horizontalx
x
x
y
![Page 59: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/59.jpg)
Capitulo 5
59
c)
4 , 2, 1,
2 14
4 ²lim lim 0,² 3 2² 3 2²
x x
x x verticalx x
x horizontalx xx xx
x
y
![Page 60: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/60.jpg)
Capitulo 5
60
d)
x
y
![Page 61: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/61.jpg)
Capitulo 5
61
1 , 3, 4,
3 41
1 ²lim lim 0,² 12² 12²
x x
x x verticalx x
x horizontalx xx xx
e)
4,
41 1 4 4lim lim lim lim 0,4² 12 44 4x x x x
x vertical
xx x x horizontalxx x xx x
x
x
y
![Page 62: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/62.jpg)
Capitulo 5
62
f)
3,
2 31 2 3 2 3lim lim lim lim 0,3² 12 33 3x x x x
x vertical
xx x x horizontalxx x xx x
x
g)
x
y
x
y
![Page 63: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/63.jpg)
Capitulo 5
63
2 2
4, 4,2 ²
2 ² ²lim lim16 16
²
x x
x x verticalx
x xx x
x
h)
2 2
3, 4,( 3)( 4)
lim lim 1,12 12
²
x x
x x x verticalx x
xx x horizontal
x x x xx
x
![Page 64: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/64.jpg)
Capitulo 5
64
i)
10
0,
lim 1,xx
x vertical
e e horizontal
x
y
![Page 65: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/65.jpg)
Capitulo 5
65
j)
lim ( 1) 1,x
xe horizontal
k)
0,x vertical
x
y
x
y
![Page 66: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/66.jpg)
Capitulo 5
66
16)
a)
x
y
![Page 67: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/67.jpg)
Capitulo 5
67
b)
x
y
![Page 68: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/68.jpg)
Capitulo 5
68
c)
x
y
x
y
![Page 69: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/69.jpg)
Capitulo 5
69
d)
e)
x
y
![Page 70: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/70.jpg)
Capitulo 5
70
f)
g)
x
y
x
y
![Page 71: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/71.jpg)
Capitulo 5
71
h)
x
y
x
y
![Page 72: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/72.jpg)
Capitulo 5
72
i)
j)
x
y
![Page 73: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/73.jpg)
Capitulo 5
73
k)
x
y
![Page 74: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/74.jpg)
Capitulo 5
74
l)
x
y
![Page 75: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/75.jpg)
Capitulo 5
75
m)
x
y
x
y
![Page 76: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/76.jpg)
Capitulo 5
76
n)
o)
p)
x
y
x
y
![Page 77: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/77.jpg)
Capitulo 5
77
5.13
1)
x
y
![Page 78: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/78.jpg)
Capitulo 5
78
2 2
22
2
( )
24
,4 2
( )4 16
'( ) 02 8
,2 8
4
44
A x r a
x ry a
y xa r
x y ly l x
l xxA x
l xxA x
l xx
lx
ly l x
b)
![Page 79: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/79.jpg)
Capitulo 5
79
2
2
2
( )( )
24
'( ) 2 0'( ) 2 0
00
( )( )
2
2
A x rA x ax ry ax y l
A x rA x ara
x ly l
temos A xA x r
x l rlr
2)
2 2
2 2
2 2 3
8
8
1
1
2 2 0
11
x ya b
yx
xa b x
axbayb
a bxy
3)
Custo adicional:
![Page 80: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/80.jpg)
Capitulo 5
80
200.2 400t t
Custo total:
( ) 380000 400C t t
Peso do boi:
( ) 60000 450kg t t
Custo do peso do boi:
[ ( )] 1080000 8100C kg t t
Mas decresce : [ ( )].0.5C kg t
[ ( )] 1080000 8100 540000 4500 ²C kg t t t t
[ ( )] ( )1080000 8100 540000 4500 ² 380000 400
' 8100 540000 8100 400 065,6
lucro C kg t C tlucro t t t tlucro tt
4)
7070
( )( ) 70( ) 70 ²'( ) 70 2 0
3535
x yy xxy f xf x x xf x x xf x xxy
5)
2( ) 2( ) ² 4 ² 4 ³'( ) ² 8 12 ² 0
2
6
V x a x xV x a x ax xV x a ax xx a
ax
6)
![Page 81: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/81.jpg)
Capitulo 5
81
3
3
( ) 2 ² 2
²
²
( ) 2 ² 2²
( ) 2 ² 2
'( ) 4 2 0²
24
A V r rh
V r hVhr
VA V r rr
VA V rr
VA V rr
Vr
Vh
7)
![Page 82: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/82.jpg)
Capitulo 5
82
2
2
2
22
2
2
4 2
16 ²
4
( ) 16 ² 4
'( ) 016 ² 4
16 ² 4
12 ²²16 ² 4 12
² 144 24 ²16 ² 4 144 24 ²
4 144 24 ² ² 16 ² 144 24 ²
148 ² 24 ³ 2304 384 16 144
y x
z l x
f x x l x
l xxf xx l x
l xxx l x
xxx x
x x xx x x
x x x x x x
x x x x x
2 4
2
24 ³12 384 2304 0
248
x x xx x
x kmx km
8)
12
12
2
12
2 2² 4 ² ²
2 2 4 ² ²4' 2
2 4 ² ²
244 ² ²
4 4 ² ² 4 ²16 ² 8 ²
2 ² 288
288
P x yx R y
p x r xxp
r x
x
r x
r x xr x
x r
y
9)
![Page 83: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/83.jpg)
Capitulo 5
83
2 2
4 4
( )2
2 2 ²
2 2 ²( )2
2 2 ² 4 ²'( ) 02 4 2 2 ²
2 2 ² ²2 2 2 ²
4 8 ² 4 44 8 ²
12
1
xyA x
y x
x xA x
x xA xx
x xx
x x xx
x
y
10)
![Page 84: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/84.jpg)
Capitulo 5
84
2
2
2 2
2 2
2 2
2
2
2
2
2
2
13
13
131'3
' 2
2
223
22 33
49 34 19 3
V R H
V r h
V R H r h
R rH H h
H R rh
RH R r
V R H rR
H R rV R H r
RH R rHV r r
R RH R rHr r
R Rr R r
Rr
V r hRH R
RVR
RV R HR
V R H
11)
![Page 85: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/85.jpg)
Capitulo 5
85
1 ²31' ²3
23
3
R rH H h
H R rh
RH R r
V rR
HV r R rR
r R
Hh
12)
² 7 ² 0 ² ( )
² 7 ² ² ²
'( ) 2 7 ² 2 1'( ) 14 2 2 ³ 2 ² ² 0
12
d x y f x
d x x x
f x x x x xf x x x x x xxy
13)
14)
15)
2 cos
2' ² cos ²
cos
4
vl senx xg
vl sen x x og
x senx
x
16)
![Page 86: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/86.jpg)
Capitulo 5
86
2 2
2 2
2 2
2 2
2 22 2
40 10018 50
1' 05018 40
15018 40
50 4018
15, 43
100 15, 43 84,56
x xt
xtx
xx
x x
x km
km
17)
2
4
4
111
² ² 1 ²
1( ) 1 ²
1 1'( ) 2 2 1 0²
2 2 2 2 0² ³
2 2 2 2 ³ 0³
2 2 2 2 ³ 01
1 2
² ² 1 ² 8
yx x
xyx
l y x
xf x xx
xf x xx x
xx xx x x
xx x x
xxy
xl y x m
18)
Pensa um pouco demais
19)
![Page 87: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/87.jpg)
Capitulo 5
87
2 2 400
2002 ( )2 200 ( )400 4 '( ) 0
100
100
r a
a rra f xr r f x
r f x
r
a
20)
3,56 6
73,52
712 6
²
1267
12² 6736' 12 ² 07
732
rh
rh
V r h
h r
V r r
V r r
r m
h m
21)
![Page 88: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/88.jpg)
Capitulo 5
88
60 12 ² 2 ³ 6 ² 18 60' 60 24 6 ² 12 18 06 ² 36 42 0² 6 7
( )1
7
L V CL x x x x xL x x x
x xx x
solução quadráticax milharx milhares
22)
2
²
² ²2
2 ² ²
²
2 ² ² ²
' 2 ² ² ²4 ³' 4 ² ² 0
2 ² ²2 ³4 ² ²² ²
2 ² 2 ² ²
23
23
V r h
hR r
h R r
V r h
V r R r
V r R rrV r R r
R rrr R r
R rR r r
r R
h R
23)
![Page 89: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/89.jpg)
Capitulo 5
89
400
3 4 ( )
400
4003 4 ( )
1600'( ) 3 0²
3403
10 3
ab
a b f x
ba
a f xa
f xa
a
b
24)
2 33
2
( , tan )2 2 2
3 3( ) 2 22
3 3( ) 4
6'( ) 4 0²
626
2
xy
xy
Area area cubo re gular tampaArea x y x
Area f x yy y
f x yy y
f xy
y
x
25)
![Page 90: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/90.jpg)
Capitulo 5
90
129
43
( ) 94( ) 93
8'( ) 123
926
992
xa
x a
Area f x a x
f x a a
f x a
a
x
y a
5.15
1)
2
2 4lim 02 1x
xx
2)
1
2lim 12 4x
xx
3)
0
2 6 6lim3 ² 14 5 5x
xx x
4)
12
4 1lim8 4x
xx
![Page 91: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/91.jpg)
Capitulo 5
91
5)
3
2 6 3 ² 11lim4 ³ 9 ² 1 26x
x xx x
6)
1
1 1lim8 ³ 6 ² 6 2 6x x x x
7)
2 6 2lim lim 03 ² 7 6x x
xx x
8)
15 ² 30 30 5lim lim lim6 ² 12 12 6x x x
x xx x
9)
4 335 140lim lim8 2 8 2x x
x xx
10)
1 2 2 1lim lim1 4 4 2x x
xx
11)
lim lim2 2
x x
x x
e ex
12)
99! 0lim lim 0x xx xe e
13)
0
1lim 1xx e senx
14)
![Page 92: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/92.jpg)
Capitulo 5
92
1 1 11
1
0 0 0 0 0
1 1² ²1lim lim lim lim lim1 1 1 1
² ³ ²
x x xx
xx x x x x
e e ex xe e
x x x x
15)
2
lim2
2x
senx
x
16)
2 ln 2lim 12 ln 2
x
xx
17)
2 2
2 2 4 1lim lim2 4 2 4 8x x
x xx x x
18)
1 1lim ln ln 1 lim lim 01x x x
x xx x
19)
2 2 2 2
1 0lim lim lim lim 1cot 2 cos cos 2x x x x
xgx x ecx senx
20)
2
2 2
2 2 2
11lim lim lim lim lim 1 1
1 1
x
x x x xx
xx x x xx x x x x
x
ee e e ee
ee e e ee
21)
0 0
22lim lim 1cos 2
x x
x x
e e
x
22)
![Page 93: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/93.jpg)
Capitulo 5
93
30 0 0
2 13 3
1 11lim 3lim 3lim1 1 1 1
3x x x
x xx
xx x
23)
24)
0 0
12lim lim 1
1 cos 2 1
x x
x x
x x
e ee e
x senx
25)
0 0 0 0
cos cos ² 2coslim lim lim lim 0cos cosx x x x
x x senx xsenxsenx senx x x
*26)
1 1
ln 1 1lim lim1 1ln
x x
xx x
x
27)
2 13 3
3 2
2 113 31 13 62
5 33 2
5 7313 62
3 1 2 1lim lim
3 1 2 1 2 3 52 1
13 2lim124 3 5
3 2 6
x x
x
x x x xx x x x x
x x
x x x
28)
4 4
2sec ² 12sec sec 2sec ²lim lim 01 4 4 1 4 4x x
x tgxx xtgx xsen x sen x
![Page 94: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/94.jpg)
Capitulo 5
94
40
40 03
3
lnln 3limln
1 1
ln 3lim 3lim 31 4 14
ln 3
x
x x
xLx x
x xLxx
x xL
L e
29)
0
0 0 0
ln lim ln
1lnln lim lim lim 01 cos
²ln 0
1
x
x x x
L senx x
x tgxsenxxL x xsenx sen x
LL
30)
1 1
1
11ln lim ln lim 1
1 1
ln 1
x xxL x
x
LL e
31)
![Page 95: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/95.jpg)
Capitulo 5
95
1 1
1 1
1 1
1ln 1 1
ln lim lim12 2cos
2 cos ²2
2 1lim cos ² lim2 1
20lim cos ² lim 0
2 cos cos2 2 2 2
ln 01
x x
x x
x x
x xL xsenx
x
xxsen x
xx x xsen x
LL
32)
1 cos²lim lim lim cos0 11 1
²x x x
senx x x
x x
33)
23
2 13 3
lim 11 2 / ²
x
x
x x
34)
0lim lim lim2 2 2
x x x x
x x x
e e e e ex
35)
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Capitulo 5
96
2
ln 2 1 2 1ln 2 lim 2 lim 0
1ln 0
1
x x
x xL
xL
L
36)
0 0
0
6
2 2ln cos 2 2cos 2ln 3lim 3lim 6lim
² 2 22sec ²26 lim 6
2ln 6
x x x
x
sen xx tg xxL
x x xx
LL e
37)
0 0 0
coscos
coslim lim lim 1cos cos cosx x x
a axxsenax a ax
axx xx x x
xsenx xx
38)
3
3 3
² 6 5 15lim³ ² 6 3 ² 3 18
2 1 5 2 1lim lim3 ² 2 6 6 3 6 2 6 5
x
x x
x x xx x x x x
xx x x x
39)
0 0 0 0 0
1ln cos ² cosln lim lim lim lim limcos 0
sec ²ln 0
1
x x x x x
x x xxL xtgx x x x
LL
40)
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Capitulo 5
97
0 0
2
1lnln 2lim 2lim 212 ln
ln 2
x x
x xLx
xL
L e
41)
4 4
1 sec ²lim lim 1cos 2 2 2x x
tgx xx sen x
42)
1 ln 1 1 lnlim lim1 1x x
x x xx
43)
0 0
2
1ln
ln lim lim 21
x
x x
x x
ee x e x
Lx
L e
5.16
1)verificar
a)
2
2
2
2
2
1'( )21''( )41'''( )81''''( )
161'''''( )
32
x
x
x
x
x
f x e
f x e
f x e
f x e
f x e
1'(0)21''(0)41'''(0)81''''(0)
161'''''(0)
32
f
f
f
f
f
12
12
12
12
12
1'(1)21''(1)41'''(1)81''''(1)
161'''''(1)32
f e
f e
f e
f e
f e
![Page 98: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/98.jpg)
Capitulo 5
98
2 3 4 51 1 1 1 11 0 0 0 0 02 4.2! 8.3! 16.4! 32.5!
P x x x x x
2 3 4 51 1 1 1 112 8 48 384 3840
P x x x x x
1 1 1 1 1 1
2 3 4 52 2 2 2 2 21 1 1 1 11 1 1 1 12 4.2! 8.3! 16.4! 32.5!
P e e x e x e x e x e x
1 1 1 1 1 1
2 3 4 52 2 2 2 2 21 1 1 1 11 1 1 1 12 8 24 384 3840
P e e x e x e x e x e x
b)
'( )''( )'''( )''''( )'''''( )
x
x
x
x
x
f x ef x ef x ef x ef x e
'( 1)''( 1)'''( 1)''''( 1)
f ef ef ef e
2
2
2
2
2
'(2)''(2)'''(2)''''(2)'''''(2)
f ef ef ef ef e
2 3 41 1 11 1 1 12! 3! 4!
P e e x e x e x e x
2
2 3 42 2 2 21 12 2 2 22! 3! 4!eP e e x x e x e x
c)
![Page 99: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/99.jpg)
Capitulo 5
99
2
3
4
5
1'( )1
1''( )1
2'''( )1
3!''''( )1
4!''''( )1
f xx
f xx
f xx
f xx
f xx
'( ) 1''( ) 1'''( ) 2''''( ) 3''''( ) 4
f xf xf xf xf x
1'( ) 221''( ) 421'''( ) 1621''''( ) 482
f
f
f
f
2 3 4
2 3 4
0 2 0 3! 00 1 0
2! 3! 4!
2 3 4
x x xP x
x x xP x
2 3 41 4 1 16 1 48 1ln 2 22 2! 2 3! 2 4! 2
P x x x x
![Page 100: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/100.jpg)
Capitulo 5
100
5
6
7
8
'( ) cos''( )'''( ) cos''''( )( ) cos( )( ) cos( )
f x xf x senxf x xf x senxf x xf x senxf x xf x senxx
5
6
7
8
' 02
'' 12
''' 02
'''' 12
02
12
02
12
f
f
f
f
f
f
f
f
2 4 6 81 1 1 112! 2 4! 2 6! 2 8! 2
P x x x x
e)
2
3
4
5
6
'( ) 2 2( ) 4cos 2( ) 8 2( ) 16cos 2( ) 32 2( ) 64cos 2
f x sen xf x xf x sen xf x xf x sen xf x x
2
3
4
5
6
'(0) 0(0) 4(0) 0(0) 16(0) 0(0) 64
ffffff
2
3
4
5
6
' 02
42
02
162
02
642
f
f
f
f
f
f
![Page 101: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/101.jpg)
Capitulo 5
101
2 4 64 16 641 0 0 02! 4! 6!
P x x x
2 4 64 16 642! 2 4! 2 6! 2
P x x x
f)
2
3
4
5
1'( )12!''( )
13!'''( )
14!''''( )
1
f xx
f xx
f xx
f xx
'(0) 1''(0) 2'''(0) 6''''(0) 24
ffff
1'(1)4
2!''(1)8
3!'''(1)16
4!''''(1)32
f
f
f
f
41 ² ³P x x x x
2 3 41 1 1 1 11 1 1 12 4 8 16 32
P x x x x
2)
a)
2
3
4
'2
2
2
2
x x
x x
x x
x x
e ef x
e ef x
e ef x
e ef x
2
3
4
' 0 0
0 1
0 0
0 1
f
f
f
f
2 4
2 4
1 11 0 02! 4!1 112 24
P x x
P x x
![Page 102: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/102.jpg)
Capitulo 5
102
4
5
cosh
5!
f x xsenhzR x
b)
1
2
3 4
4 4 3
sec ²
2sec ²
2sec 4sec ² ²
16sec 8sec ²
f x x
f x xtgx
f x x xtg x
f x xtgx xtg x
1
2
3
4 4 3
1
0
2
16sec 8sec ²
f
f
f
f z ztgz ztg z
3
3
203!
13
P x x
P x x
4 3
416sec 8sec ²4!
ztgz ztg zR x
c)
11 2
32 2
53 2
74 2
12
14
381516
f x x
f x x
f x x
f x x
1
2
3
4
112
114
318
15116
f
f
f
f
2 31 1 31 1 1 12 4.2! 8.3!
P x x x
7
47 242
15 115 116.4! 384
z xR z x
![Page 103: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/103.jpg)
Capitulo 5
103
d)
2
2 2
2 2 2
2 2 2 2 2 2
2 2 2 2
2 2 2 2 2 2
1
2 2
3 3
4 4 2 2
5 5 3 3
3
0 2
0 4 2
0 8 8 4
0 16 24 16 8 8 ² 4
0 64 64 48 48
32 32 8 16 16 ³ 8
x
x x
x x x
x x x x x x
x x x x
x x x x x x
f xe
f x e e
f x e x e xe
f x e x e x e e x e e
f x e x e x e x e
x e x e xe xe x e xe
2 4
2 4
2 121 0 02! 4!
112
P x x
P x x
2 2 25 3 564 112 160
5!
x x xx e x e x e xR
R não bateu
3)
1 1 1 1 0,6832 8 24 64
P
5
2
4! 1 0,2215! 1
2
R
4)
![Page 104: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/104.jpg)
Capitulo 5
104
1
2
3
4
5
6
7
cos
cos
cos
f x senx
f x x
f x senx
f x x
f x senx
f x x
f x senx
1
2
3
4
5
6
0
1
0
1
0
1
f
f
f
f
f
f
2 4 61 1 12! 4! 6!
P x x x
2 4 6
2 4 6
1 5 1 5 1 502! 6 4! 6 6! 6
1 1 1 0,133972! 6 4! 6 6! 6
P
P
5 51 cos6 65 5cos 1 0,13397 1 0,866036 6
f
f
27 0,0000275.6
R f z senz z
onde z
5)
senx
![Page 105: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/105.jpg)
Capitulo 5
105
1
2
3
4
( ) cos( )( ) cos( )
f x xf x senxf x xf x senx
'(0) 1''(0) 0'''(0) 1
fff
Sen(a+h)
sena
3
3
3
10 03!
16
16
P x x
P a a
P a h a h
cosx
2
3
4
'( )( ) cos( )( ) cos
f x senxf x xf x senxf x x
2
3
'(0) 0(0) 1(0) 0
fff
Cosa
3
3
11 03!116
P x
P a
![Page 106: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/106.jpg)
Capitulo 5
106
3 3 2
3 2 2 3 3 2
3 2 2
1 1 116 6 2
1 3 3 1 16 6 6 6 6 2
1 1 16 2 2 3
a h a h a a h a
hh a a h ah h a h a
hh ah h a
6)
'( )2
'( )2
'( )2 ²
'(0) 01'(0)
'(0) 0
1 ²2!
x xa a
x xa a
x xa a
e ef x
e ef xa
e ef xa
f
fa
f
p a xa
7)
![Page 107: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/107.jpg)
Capitulo 5
107
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Capitulo 5
108
![Page 109: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/109.jpg)
Capitulo 5
109
![Page 110: capitulo 5 Flemming Resolvido Calculo A 5ª edição](https://reader033.vdocuments.net/reader033/viewer/2022050921/5535dab94a7959a0138b4771/html5/thumbnails/110.jpg)
Capitulo 5
110