Create assignment, 57321, Homework 50, Feb 28 at 12:42 pm
1
This printout should have 13 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
be±ore answering.
The due time is Central
time.
CalC2b04a
48:02, calculus3, multiple choice,
>
1 min,
normal.
001
Below is the graph o± a ±unction
f
.
2
4
6

2

4

6
2
4
6
8

2

4
Use the graph to determine
lim
x
→
4
f
(
x
)
.
1.
limit = 9
2.
limit = 4
3.
limit = 6
4.
limit = 8
5.
limit does not exist
correct
Explanation:
From the graph it is clear the
f
has a le±t
hand limit at
x
= 4 which is equal to 8; and
a right hand limit which is equal to 6. Since
the two numbers do not coincide, the
limit does not exist
.
keywords: defnition o± limit, graph, domain,
range, limit at jump discontinuity
CalC2e21a
48:04, calculus3, multiple choice,
>
1 min,
normal.
002
Find all values o±
x
at which the ±unction
f
defned by
f
(
x
) =
x

4
x
2
+ 2
is not continuous?
1.
x
= 4
2.
x
=

√
2
3.
x
= 4
,

√
2
4.
no values o±
x
correct
5.
x
=
√
2
6.
x
=

√
2
,
√
2
Explanation:
Because
f
is a rational ±unction it will ±ail
to be continuous only at zeros o± the denomi
nator. Since there are no real solutions to
x
2
=

2
,
the ±unction is continuous everywhere; put
another way,
f
±ails to be continuous at
no values o±
x
.
keywords: rational ±unction, continuous
CalC3a01e
49:01, calculus3, multiple choice,
>
1 min,
wordingvariable.
003
I±
f
(
x
) =

5
x
2
+ 3
x ,
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2
which of the following determines the deriva
tive of
f
(
x
)?
1.
lim
h
→
0

5(
x
+
h
)
2
+ 3(
x
+
h
) + 5
x
2

3
x
h
correct
2.

5(
x
+
h
)
2
+ 3(
x
+
h
) + 5
x
2

3
x
h
3.
lim
x
→
0
µ

5
x
2
+ 3
x
+
hx
2

x
h
¶
4.

5(
x
+
h
)
2
+ 3(
x
+
h
)

5
x
2
+ 3
x
h
5.
lim
h
→
0
µ

5
x
2
+ 3
x
+
h
+
x
2

x
h
¶
6.
lim
x
→
0

5(
x
+
h
)
2
+ 3(
x
+
h
) + 5
x
2

3
x
h
Explanation:
When
f
(
x
) =

5
x
2
+ 3
x
then
f
(
x
+
h
) =

5(
x
+
h
)
2
+ 3(
x
+
h
)
so the derivative of
f
(
x
) is given by
f
0
(
x
) = lim
h
→
0
f
(
x
+
h
)

f
(
x
)
h
= lim
h
→
0

5(
x
+
h
)
2
+ 3(
x
+
h
) + 5
x
2

3
x
h
.
keywords: limit, derivative
CalC3b06a
49:01, calculus3, multiple choice,
>
1 min,
normal.
004
If
f
is a function on (

8
,
8) having
3
6

3

6
3
6

3

6
as its graph, which of the following is the
graph of the derivative of
f
?
1.
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 Spring '06
 McAdam
 Calculus, Derivative, lim, 5x2

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