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Nanda, Gagan – Homework 2 – Due: Sep 2 2004, 3:00 am – Inst: R Gompf
3
4.
I, III only
5.
each of I, III
6.
I, II only
009
(part 1 of 2) 10 points
(i) Which of the following statements is 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
2.
II only
3.
neither I nor II
4.
Io
n
l
y
010
(part 2 of 2) 10 points
(ii) Which of the following statements is
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
3.
both I and II
4.
neither I nor II
011
(part 1 of 1) 10 points
Below is the graph of a function
f
.
246
−
2
−
4
−
6
2
4
6
8
−
2
−
4
Use the graph to determine lim
x
→
4
f
(
x
).
1.
lim
x
→
4
f
(
x
)=12
2.
lim
x
→
4
f
(
x
)=6
3.
lim
x
→
4
f
(
x
)=4
4.
lim
x
→
4
f
(
x
)=9
5.
lim
x
→
4
f
(
x
) does not exist
012
(part 1 of 1) 10 points
Below is the graph of a function
f
.
Nanda, Gagan – Homework 2 – Due: Sep 2 2004, 3:00 am – Inst: R Gompf
4
−
2
−
4
−
6
2
4
6
8
−
2
−
4
Use the graph to determine lim
x
→−
3
f
(
x
).
1.
lim
x
3
f
(
x
)=8
2.
lim
x
3
f
(
x
3.
lim
x
3
f
(
x
)=1
4.
lim
x
3
f
(
x
) does not exist
5.
lim
x
3
f
(
x
013
(part 1 of 1) 10 points
Below is the graph of a function
f
.
−
2
−
4
−
6
2
4
6
8
−
2
−
4
Use the graph to determine the right hand
limit
lim
x
→
3+
f
(
x
)
.
1.
lim
x
→
3+
f
(
x
−
4
2.
the limit does not exist
3.
lim
x
→
3+
f
(
x
4.
lim
x
→
3+
f
(
x
7
2
5.
lim
x
→
3+
f
(
x
014
(part 1 of 1) 10 points
Belowisthegraphofafunction
f
.
−
2
−
4
−
6
2
4
6
8
−
2
−
4
Use the graph to determine the left hand limit
lim
x
→
3
−
f
(
x
)
.
1.
lim
x
→
3
−
f
(
x
3
2
2.
lim
x
→
3
−
f
(
x
3.
lim
x
→
3
−
f
(
x
)=3
4.
lim
x
→
3
−
f
(
x
−
4
Nanda, Gagan – Homework 3 – Due: Sep 9 2004, 3:00 am – Inst: R Gompf
5
exists, and if it does, Fnd its value.
1.
limit does not exist
2.
limit = 6
3.
limit =
−
7
4.
limit =
−
6
5.
limit = 7
020
(part 1 of 1) 10 points
±ind the value of
lim
x
→
0
x
√
16 + 3
x
−
4
.
1.
limit =
3
8
2.
limit =
4
3
3.
limit =
3
4
4.
limit = 0
5.
limit =
8
3
6.
limit =
∞
021
(part 1 of 1) 10 points
If the graph of
f
is
2
4
6
8
10
12
2
4
6
8
−
2
−
4
−
6
Fnd the value of the left hand limit
lim
x
→
9
−
x
−
9

x
−
9

f
(
x
)
.
1.
limit does not exist
2.
limit =
−
3
3.
limit =
−
5
4.
limit = 4
5.
limit = 3
6.
limit =
−
4
022
(part 1 of 1) 10 points
Determine if the limit
lim
x
→
4+
5

x
−
4

x
2
+3
x
−
28
exists, and if it does, compute its value.
1.
limit =
−
5
11
2.
limit =
5
11
3.
limit does not exist
Nanda, Gagan – Homework 4 – Due: Sep 16 2004, 3:00 am – Inst: R Gompf
3
Use this graph to determine all the values of
x
on (
−
7
,
7) at which
f
is discontinuous.
1.
x
=
−
1
,
1
2.
none of these
3.
x
=1
4.
x
=
−
1
5.
no values of
x
009
(part 1 of 1) 10 points
Find all values of
x
at which the function
f
de±ned by
f
(
x
2
1
−
cos
x
fails to be continuous.
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This note was uploaded on 02/28/2010 for the course M 56200 taught by Professor Radin during the Fall '09 term at University of Texas at Austin.
 Fall '09
 RAdin

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