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Solutions to Practice Quiz ID
Problem I:
a)
δ
=
ε
2
will do the job.
b) The frst is true, the second is False, take
a
=

2 and
b
= 1.
c)
x >
1 and
x <

1.
d)
‘
(
x
) = 5
x

8
e)
‘
(
x
) =
x/
3 + 4
/
3
Problem II:
a) 3
/
2.
b) Note that sin(2
x
) =

sin(2(
x

π/
2)) and hence the limit is

2.
c) Does not exist.Numerator tends to 1 and denominator tends to 0.
d) 0
e) Note that cos(
x
) =

sin(
x

π/
2). Hence the limit is

1.
Problem III:
a)

√
3
/
2
< x <
√
3
/
2
b)
g
(
h
) =

h

√
1

h
2
(
√
1

h
2
+ 1)
c) There are a number oF reasonable solutions, one oF them is:
δ
= min(1
/
√
2
,
(1 + 1
/
√
2)
ε
)
since
g
(
h
)
≤
1
/
√
2
(1
/
√
2)(1
/
√
2 + 1)
For

h
 ≤
1
/
√
2.
Problem IV:
Set
P
(
n
) =

1 + 2
2

3
2
+
···
+ (

1)
n
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 Fall '08
 N/A
 Calculus

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