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Section 5.9 (Homework)
1. [SCalcCC2 5.9.02.]
2/2 points
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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
0.7811
,
0.8678
,
0.8632
, and
0.9570
, and the same number of subintervals
were used in each case.
(a) Which rule produced which estimate?
L
n
= 0.9570
0.9570
T
n
=
0.8678
0.8678
M
n
=
0.8632
0.8632
R
n
=
0.7811
0.7811
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0.8632
0.8632
(smaller approximation)
0.8678
0.8678
(larger approximation)
2.
4.25/4.25 points
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[SCalcCC2 5.9.04.] Draw the graph of
f
(
x
) = sin(
x
2
/2) in the viewing rectangle [0,1] by [0,0.5]
and let
I
be the following.
(a) Use the graph to decide whether
L
2
,
R
2
,
M
2
, and
T
2
underestimate or overestimate
I
.
L
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 Spring '10
 LeslieKurtz
 Calculus, Approximation

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