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Exam 2 – Take Home
Name: ____________, _____________
(last)
(first)
Last Name
f
(
x
)
Graph of
f
(
x
)
Graph of
f
″
(
x
)
Evaluate
A
x
e
–
x
2
1
)
2
ln(
1
lim
2



→
x
x
x
B–C
x
e
–2
x
x
x
x
ln
1
lim
0
+
+
→
D–H
x
e
–
x
/2
x
x
x
/
1
0
)
(cos
lim
→
KM
x
e
–
x
2
/2
x
x
x
)
2
(sin
lim
0
→
N–O
x
e
–
x
2
/4
x
x
x
2
0
)
(tan
lim
→
P–R
x
2
e
–
x
1
0
)
/
1
(
lim

→
x
e
x
x
SY
x
2
e
–2
x
)
1
ln(
)
1
(
lim
1


+
→
x
x
x
Do them according to your last name:
1. Trapezoidal Rule (First 3 Columns)
a)
Use
n
= 5 to approximate the area of your region by Trapezoidal Rule
from
x
= 0 to
x
= 5. [Hint:
you must find
h
0
,
h
1
,
h
2
,
h
3
,
h
4
, and
h
5
first]
b)
Use the graph of
f
″
(
x
) to get
K
first and then use it to find the maximum error can be made, i.e.,
find 
E
T
max
.
c)
Find the exact area of the region, i.e., evaluate your integral. [Hint: some need
u
substitution, while
others need integration by parts.]
d)
Find the actual error made, i.e., 
E
T
act

e)
Is your actual error less than the maximum error?
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This note was uploaded on 10/28/2011 for the course MATH 795 taught by Professor Thompson during the Spring '11 term at CUNY Hunter.
 Spring '11
 Thompson
 Algebra, Algebraic Topology

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