1. Given the rate of change (derivative) below, evaluate the following:
2
0
2
4
6
4
10
5
x
0
6
15
i
0

1
f
(
t
)
dt
= 1
i
2

1
f
(
t
)
dt
= 9
i
2
0
f
(
t
)
dt
= 8
i
0

4
f
(
t
)
dt
=

8
i
5

4
f
(
t
)
dt
= 14
i
15
0
f
(
t
)
dt
= 32
If
F
(0) = 8 and
F
p
(
t
) =
f
(
t
) determine the following:
F
(2) = 16
F
(4) = 27
F
(

4) = 16
F
(15) = 40
With
F
(0) = 8, sketch
F
(
t
), the antiderivative of
f
(
t
), labeling the points (4
, F
(4)),
(

1
, F
(

1)), (2
,
(
F
(2)), (5
, F
(5)). Make sure to show the concavity of
F
.
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View Full Document2. Draw the graph of
f
(
x
) =
10
x
labeling the
x
axis from
x
= 1 to
x
= 6. Approximate
i
6
1
10
x
dx
using:
(a) the Right Riemann Sum with 5 equal partitions.
RRS
(
n
= 5) =
p
10
2
P
(1) +
p
10
3
P
(1) +
p
10
4
P
(1) +
p
10
5
P
(1) +
p
10
6
P
(1)
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 Fall '08
 Chen
 Calculus, Derivative, Rate Of Change, Leftwing politics, Riemann sum, right Riemann sum

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