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Pham, Quoc – Homework 2 – Due: Jan 30 2007, 3:00 am – Inst: Eric Katerman
1
This
printout
should
have
19
questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
The due time is Central
time.
001
(part 1 oF 1) 10 points
Rewrite the sum
n
3+
‡
1
9
·
2
o
+
n
6+
‡
2
9
·
2
o
+
...
+
n
18+
‡
6
9
·
2
o
using sigma notation.
1.
6
X
i
= 1
n
i
+
‡
3
i
9
·
2
o
2.
9
X
i
= 1
3
n
i
+
‡
3
i
9
·
2
o
3.
9
X
i
= 1
3
n
i
+
‡
i
9
·
2
o
4.
9
X
i
= 1
n
3
i
+
‡
i
9
·
2
o
5.
6
X
i
= 1
3
n
i
+
‡
i
9
·
2
o
6.
6
X
i
= 1
n
3
i
+
‡
i
9
·
2
o
correct
Explanation:
The terms are oF the Form
n
3
i
+
‡
i
9
·
2
o
,
with
i
= 1
,
2
, ... ,
6. Consequently, in sigma
notation the sum becomes
6
X
i
= 1
n
3
i
+
‡
i
9
·
2
o
.
keywords: Stewart5e, summation notation,
002
(part 1 oF 1) 10 points
Estimate the area,
A
, under the graph oF
f
(
x
) =
5
x
on [1
,
5] by dividing [1
,
5] into Four equal
subintervals and using right endpoints.
Correct answer: 6
.
417 .
Explanation:
With Four equal subintervals and right end
points as sample points,
A
≈
n
f
(2) +
f
(3) +
f
(4) +
f
(5)
o
1
since
x
i
=
x
*
i
=
i
+ 1. Consequently,
A
≈
6
.
417
.
keywords: Stewart5e, area, rational Function,
Riemann sum,
003
(part 1 oF 1) 10 points
Cyclist Joe accelerates as he rides away
From a stop sign. His velocity graph over a 5
second period (in units oF Feet/sec) is shown
in
1
2
3
4
5
4
8
12
16
20
Compute best possible upper and lower es
timates For the distance he travels over this
period by dividing [0
,
5] into 5 equal subinter
vals and using endpoint sample points.
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View Full DocumentPham, Quoc – Homework 2 – Due: Jan 30 2007, 3:00 am – Inst: Eric Katerman
2
1.
39 ft
<
distance
<
59 ft
2.
43 ft
<
distance
<
57 ft
3.
39 ft
<
distance
<
57 ft
correct
4.
41 ft
<
distance
<
59 ft
5.
39 ft
<
distance
<
61 ft
6.
41 ft
<
distance
<
61 ft
7.
43 ft
<
distance
<
59 ft
8.
43 ft
<
distance
<
61 ft
9.
41 ft
<
distance
<
57 ft
Explanation:
The distance Joe travels during the 5 sec
ond period is the area under the velocity
graph and above [0
,
5].
Since Joe’s speed
is increasing, the best possible lower estimate
occurs taking left hand endpoints as sample
points and the area of the rectangles shown in
1
2
3
4
5
4
8
12
16
20
On the other hand, the best upper estimate
will occur taking right hand endpoints and
the area of the rectangles shown in
1
2
3
4
5
4
8
12
16
20
Consequently, reading oF values from the
graphs to compute the height of the rect
angles, we see that
39 ft
<
distance
<
57 ft
.
keywords:
004
(part 1 of 1) 10 points
Stewart Section 5.1, Example 3(a), page 321
Decide which of the following regions has
area =
lim
n
→ ∞
n
X
i
= 1
π
5
n
tan
iπ
5
n
without evaluating the limit.
1.
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