Gaspar, Adrian – Homework 1 – Due: Sep 4 2007, 3:00 am – Inst: MC Caputo
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The due time is Central
time.
001
(part 1 of 1) 10 points
Find the most general function
f
such that
f
00
(
x
) = 48 cos 4
x .
1.
f
(
x
) =

3 cos 4
x
+
Cx
+
D
2.
f
(
x
) = 4 sin 4
x
+
Cx
+
D
3.
f
(
x
) = 3 cos
x
+
Cx
+
D
4.
f
(
x
) = 3 sin
x
+
Cx
+
D
5.
f
(
x
) =

4 sin
x
+
Cx
2
+
D
6.
f
(
x
) =

4 cos 4
x
+
Cx
2
+
D
002
(part 1 of 1) 10 points
Find
f
(
x
) on
(

π
2
,
π
2
)
when
f
0
(
x
) = 5 + tan
2
x
and
f
(0) = 5.
1.
f
(
x
) = 6

4
x

sec
x
2.
f
(
x
) = 5 + 4
x
+ tan
x
3.
f
(
x
) = 4 + 5
x
+ sec
2
x
4.
f
(
x
) = 4 + 5
x
+ sec
x
5.
f
(
x
) = 5

4
x

tan
x
6.
f
(
x
) = 5 + 4
x
+ tan
2
x
003
(part 1 of 1) 10 points
Determine
f
(
t
) when
f
00
(
t
) = 4(3
t
+ 2)
and
f
0
(1) = 4
,
f
(1) = 5
.
1.
f
(
t
) = 2
t
3
+ 4
t
2

10
t
+ 9
2.
f
(
t
) = 2
t
3

8
t
2
+ 10
t
+ 1
3.
f
(
t
) = 6
t
3

8
t
2
+ 10
t

3
4.
f
(
t
) = 6
t
3
+ 8
t
2

10
t
+ 1
5.
f
(
t
) = 6
t
3
+ 4
t
2

10
t
+ 5
6.
f
(
t
) = 2
t
3

4
t
2
+ 10
t

3
004
(part 1 of 1) 10 points
Find the unique antiderivative
F
of
f
(
x
) =
e
3
x
+ 3
e
2
x
+ 4
e

x
e
2
x
for which
F
(0) = 0.
1.
F
(
x
) =
e
x
+ 3
x

e

x
2.
F
(
x
) =
e
x

3
x
+
4
3
e

x

1
3
3.
F
(
x
) =
e
x
+ 3
x

4
3
e

3
x
+
1
3
4.
F
(
x
) =
1
3
e
3
x

3
x
+
e

x

1
5.
F
(
x
) =
1
3
e
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 Fall '08
 RAdin
 Calculus, Acceleration, Velocity, Gaspar, uniform acceleration

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