Trabalho 1 - T490 - Gabarito

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO GRANDE DO SUL 
Faculdade de Matemática – Departamento de Matemática 
Cálculo Diferencial e Integral II – Turma: 490 
Professora: Gabriela Wehr 
 
GABARITO – TRABALHO 1 
 
1. 
a. 
cxxdxxdxxdx
x
x




2
1
2
3
2
1
2
1
4223
)23(
 
 
b. 
  cxxcuuduuuduuudxxx 





 
89
89
7877 )2(
4
3
)2(
3
1
8
2
9
323)2(3)2(3
 
 
c. 
cxdusenudx
x
xsen
xxdxxtgxx   )cos(3
1
.
3
1
)cos(
)(
).cos(.)()cos( 3
3
3
32332
 
 
d. 
ceduedxexdx
e
x xux
x
  
33
3
3
1
3
1
.2
2 
 
2. 
ceedteetP tttt  
03,01,003,01,0 50002000)150200()(
 
000.203
000.20050002000)0(


c
cP
 
000.20350002000)( 03,01,0   tt eetP
 
152.206000.20350002000)12( 12.03,012.1,0  eeP
bactérias 
 
3. 
)3()2cos(
2
2
xsenx
dx
yd

, 
2)(' y
 e 
1)( y
 
 
c
xxsen
xy
dxxsenxxy

 
3
)3cos(
2
)2(
)('
)3()2cos()('
. 
 
3
7
2
3
)3cos(
2
)2(
'


c
c
sen
y


 
 2 
3
7
3
)3cos(
2
)2(
)(' 
xxsen
xy
 
cx
xsenx
xy
dx
xxsen
xy







 
3
7
9
)3(
4
)2cos(
)(
3
7
3
)3cos(
2
)2(
)(
 


3
7
4
3
1
3
7
9
)3(
4
)2cos(
)(


c
c
sen
y
 
4
3
3
7
3
7
9
)3(
4
)2cos(
)(  xxsenxxy
 
 
4. 
 
 
   
22
122424120
6
24
6
4
3
66
2
3
6
2
6
2
0
22
0
4
2
2
0
3
0
4
2
0
3
0
4








































x
xx
x
x
dxxxdx
x
dxxxdx
x
xA
 
 
5. 
 
 
  ..
2
9
3
8
24
3
1
2
1
2
32
22
1
2
321
2
2 au
xx
xdxxxA 













