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Classwork IV
Sections 2.8, 2.9
lim
x
→∞
x
2
5

x
3
=
(This is 2.8.2).
lim
t
→∞
t
t

5
=
(2.8.4).
lim
x
→∞
±
√
2
x
2
+ 3

√
2
x
2

5
²
=
(2.8.17).
lim
t
→
1

2
t
2

t

2

3
t
+ 1
=
lim
t
→
1
+
2
t
2

t

2

3
t
+ 1
=
lim
t
→
1
2
t
2

t

2

3
t
+ 1
=
Find the horizontal and vertical asymptotes for the graph of
f
(
x
) =
3
x
+ 1
and sketch
its graph. (2.8.37).
Let
f
(
x
) =
1
x

1
. Then
f
(

2) =

1
3
and
f
(2) = 1. Is there a number
c
,

2
≤
c
≤
2 such
that
f
(
c
) = 0? Explain. (2.9.46).
Let
f
(
x
+
y
) =
f
(
x
) +
f
(
y
) for all
x
and
y
in
R
and suppose that
f
is continuous at
x
= 0. Prove that
f
is continuous everywhere. (2.9.49a).
Find
k
such that
f
(
x
) =
³
kx
+ 1 if
x
≤
2
kx
2
if
x >
2
is continuous.
Where is
g
(
x
) =
x
if
x
≤
1
x
2
if 1
< x
≤
2
sin
x
if
x >
2
continuous?
Suppose
g
(
x
) =

f
(
x
)

is continuous. Is it necessarily true that
f
(
x
) is continuous? Prove it
or give a counterexample. (2.9.55).
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 Summer '08
 Any
 Calculus

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