Homework # 2
Due: 5/30/06
1. Use the graph to find the following limits:
lim
x
→
2
+
f
(
x
)
lim
x
→
2

f
(
x
)
lim
x
→
2
f
(
x
)
lim
x
→
0
f
(
x
)
lim
x
→
1
f
(
x
)
2. Sketch the graph of a function that satisfies all of the given conditions:
lim
x
→
0

f
(
x
) = 1
lim
x
→
0
+
f
(
x
) = 2
f
(0) = 1
lim
x
→
1
f
(
x
) = 1
f
(
x
) is undefined
3. Use the limit laws to find the following limits. Justify each step.
(a)
lim
x
→
3
(
x
2
+ 3)(
x

4)
lim
x
→
3
(
x
2
+ 3)(
x

4) =
lim
x
→
3
(
x
2
+ 3)
lim
x
→
3
(
x

4)
Law 4
=
lim
x
→
3
x
2
+ lim
x
→
3
3
lim
x
→
3
x

lim
x
→
3
4
Laws 1 and 2
=
lim
x
→
3
x
2
+ 3
lim
x
→
3
x

4
Law 7
=
(
(

3)
2
+ 3
)
(

3

4)
Law 9
=

84
(b) lim
x
→
2
x

2
x
3

8
First,
x

2
x
3

8
=
1
x
2
+2
x
+4
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lim
x
→
2
1
x
2
+ 2
x
+ 4
=
lim
x
→
2
1
lim
x
→
2
(
x
2
+ 2
x
+ 4)
Law 5
=
lim
x
→
2
1
lim
x
→
2
x
2
+ lim
x
→
2
2
x
+ lim
x
→
2
4
Laws 1,2
=
lim
x
→
2
1
lim
x
→
2
x
2
+ 2 lim
x
→
2
x
+ lim
x
→
2
4
Law 3
=
1
lim
x
→
2
x
2
+ 2 lim
x
→
2
x
+ 4
Law 7
=
1
2
2
+ 2(2) + 4
Law 9
=
1
12
Note: I don’t think I intended for the denominator to be
x
3

8. I think I wanted
x
3

2.
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 Spring '08
 varies
 Limits, Limit, lim, #, Limit of a function, Halle Berry, Famke Janssen

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