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Section 5.9
(Homework)
SMALL BRIAN DIXON
MA 241, section 009, Fall
2005
Instructor: Drew Pasteur
North Carolina State
University
About this Assignment
Due:
Thursday, September 8, 2005 11:12 PM EDT
Current Score:
14.25 out of 14.25
Question Score
Description
Approximate
Integration
pts
subs
1 0.25/0.25 4/20
2 0.25/0.25 2/20
3 0.25/0.25 3/20
4 0.25/0.25 1/20
5
0.5/0.5
3/20
6
0.5/0.5
2/20
2/2
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Notes
1.
[SCalcCC2 5.9.02.]
The left, right, Trapezoidal, and Midpoint Rule
approximations were used to estimate the following where
f
is the
function whose graph is shown below it.
The estimates were
0.7816
,
0.8676
,
0.8631
, and
0.9530
, and the
same number of subintervals were used in each case.
(a) Which rule produced which estimate?
L
n
=
0.9530
[ 0.9530 ]
T
n
=
0.8676
[ 0.8676 ]
M
n
=
0.8631
[ 0.8631 ]
R
n
=
0.7816
[ 0.7816 ]
(b) Between which two approximations does the true
value of the integral lie?
0.8631
[ 0.8631 ]
(smaller approximation)
0.8676
[ 0.8676 ]
(larger approximation)
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pts
subs
1 0.25/0.25 1/20
2 0.25/0.25 2/20
3 0.25/0.25 1/20
4 0.25/0.25 2/20
5
.2/.2
1/20
6
.2/.2
3/20
7
.2/.2
5/20
8
.2/.2
4/20
9
.2/.2
2/20
10
0.5/0.5
1/20
11
0.5/0.5
1/20
12
0.5/0.5
1/20
13
0.5/0.5
1/20
14 0.25/0.25 3/20
4.25/4.25

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