Student Name:
Sections 5.1 (Due: Tuesday, 11/13)
Notice:
NO CLASS ON MONDAY, 11/12
Description
:
This homework will help you understand the area under a curve as a limit of a sum of
areas of thin rectangles. It is important to know how to approximate this area using the right hand,
left hand and midpoint sums.
Show all work to get full credit.
1)
Do the following.
(a) Estimate the area under the graph of
f
(
x
) =
7
+
4
x
2
from
x
= 1 to
x
= 2 using three rectangles
and right endpoints.
R
3
=
Improve your estimate by using six rectangles.
R
6
=
(b) Repeat part (a) using left endpoints.
L
3
=
L
6
=
(c) Repeat part (a) using midpoints.
M
3
=
M
6
=
2)
The speed of a runner increased steadily during the first three seconds of a race. Her speed at
halfsecond intervals is given in the table. Find lower and upper estimates for the distance,
d
that
she traveled during these three seconds.
t
(s)
0
0.5 1.0
1.5
2.0
2.5
3.0
v
(ft/s)
0
5.7 9.2 15.5 18.8 19.4
20
d
(lower estimate)
d
(upper estimate)
3)
The area
A
of the region
S
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 Fall '08
 Noohi
 Calculus, Derivative, Angles, Limit

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