MAT 125A Homework 3
M.Fukuda
Please submit your answers at the discussion session on October 25th Thursday.
You can use theorems in the lecuture unless otherwise stated. When you do so write those
statements clearly instead of quoting them by numbers.
1. Let
s,t
∈
R
and
f
1
,f
2
: (
s,t
)
→
R
.
Take
a
∈
(
s,t
) and, suppose lim
x
→
a

f
1
(
x
) and
lim
x
→
a

f
2
(
x
) exist. Let
L
i
= lim
x
→
a

f
i
(
x
) for
i
= 1
,
2.
1) Suppose
L
1
,L
2
∈
R
. Then, show that
L
= lim
x
→
a

f
1
(
x
)+
f
2
(
x
) exits and
L
=
L
1
+
L
2
.
2) Suppose
L
1
∈
R
and
L
2
=
∞
. Then, does the limit
L
= lim
x
→
a

f
1
(
x
) +
f
2
(
x
) exist?
Prove your idea.
3) Suppose
L
1
=
∞
and
L
2
=
∞
. Then, does the limit
L
= lim
x
→
a

f
1
(
x
)+
f
2
(
x
) exist?
Explain your idea briefly.
2. Find the redious of convergence and determine the exact interval of convergence.
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 Fall '07
 Fukuda
 li, 3 M, MAT 125A Homework, Suppose L1

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