Project 7
MAC 2311
1. Write the domain of
f
(
x
) =
4
x

x
x

2

8
x
.
Rewrite
f
(
x
)
as a simplified rational function in lowest terms, including restrictions on the
domain. Then, use a number line to find the intervals on which
f
(
x
)
is positive and those on
which it is negative. This is one way to distinguish between limits that are
∞
or
∞
.
Evaluate the following limits, and graph
f
(
x
)
on the axes below.
lim
x
→
2

f
(
x
) =
lim
x
→
2
+
f
(
x
) =
lim
x
→
0

f
(
x
) =
lim
x
→
0
+
f
(
x
) =
lim
x
→
4

f
(
x
) =
lim
x
→
4
+
f
(
x
) =
Hint: Be mindful of your domain (watch for holes), and use shifting, reflecting, etc. along
with the fact that
x
+
b
x
+
a
=
x
+
a
x
+
a
+
b

a
x
+
a
=
1 +
b

a
x
+
a
2. If possible, find the value of the constant
c
so that
lim
x
→
2
h
(
x
)
exists for the piecewisedefined
function below.
h
(
x
) =
x
2

4

x
2

2
x

x <
2
x
+
cx
2
x >
2
What is
lim
x
→
0
h
(
x
)
?
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3. In the theory of relativity, the mass
m
of a particle with speed
v
is: (
*
)
m
=
m
o
p
1

(
v/c
)
2
,
where
m
o
is the rest mass of the particle and
c
is the speed of light in a vacuum.
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 Spring '08
 ALL
 Calculus, Kinetic Energy, Mass, Special Relativity, Tan, limit lim, 2 k

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