handa (nh5757) – Limits – bormashenko – (54880)
1
This printout should have 13 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001 (part 1 of 2) 10.0 points
Which oF the Following statements are true
For all values oF
c
?
I.
lim
x
→
c
f
(
x
)=0=
⇒
lim
x
→
c

f
(
x
)

=0
.
II.
lim
x
→
c

f
(
x
)

=0=
⇒
lim
x
→
c
f
(
x
)=0
.
1.
Both I and II
correct
2.
Neither I nor II
3.
Io
n
l
y
4.
II only
Explanation:
IF
f
(
x
)isc
loseto0
,then

f
(
x
)

also must
be close to 0. Conversely, iF

f
(
x
)

is close to
0,
f
(
x
)mustalsobecloseto0.ThereFore
Both I and II are true
.
002 (part 2 of 2) 10.0 points
Which oF the Following statements are true
For all
c
and all
L
?
I. lim
x
→
c
f
(
x
)=
L
=
⇒
lim
x
→
c

f
(
x
)

=

L

.
II. lim
x
→
c

f
(
x
)

=

L

=
⇒
lim
x
→
c
f
(
x
L.
1.
II only
2.
n
l
y
correct
3.
Neither I nor II
4.
Both I and II
Explanation:
IF
f
(
x
)i
sc
lo
seto
L
,th
en

f
(
x
)

must be
close to

L

no matter what the value oF
L
is.
So I is true.
But II not true For all
L
and
c
.Toseetha
t
,
let
f
(
x
x
,
c
=

2and
L
=2.Then
lim
x
→
c

f
(
x
)

=l
i
m
x
→
2

x

=2=

L

.
On the other hand,
lim
x
→
c
f
(
x
)= l
im
x
2
x
=

2
±
=
L.
Consequently,
Only I is true
.
003
10.0 points
Below is the graph oF a Function
f
.
24

2

4
2
4

2

4
Use the graph to determine lim
x
→
2
f
(
x
).
1.
limit = 0
2.
limit = 1
3.
does not exist
4.
limit =

2
correct
5.
limit =

1
Explanation:
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View Full Documenthanda (nh5757) – Limits – bormashenko – (54880)
2
From the graph it is clear that the limit
lim
x
→
2

f
(
x
)=

2
,
from the left and the limit
lim
x
→
2+
f
(
x

2
,
from the right exist and coincide in value.
Thus the twosided limit exists and
lim
x
→
2
f
(
x

2
.
004
10.0 points
Suppose
lim
x
→
5
f
(
x
)=4
.
Which of the following statements are true
without further restrictions on
f
?
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 Spring '10
 Gualdini
 Limits, Limit, lim

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