Exam+3B+Solution+%281%29
pdf
keyboard_arrow_up
School
George Mason University *
*We aren’t endorsed by this school
Course
422
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
14
Uploaded by juliasshen
Calculus
I:
MAC2311
Name:
Kfl
9/
Fall
2023
¢
Exam
3
B
Section:
11/14/2023
Time
Limit:
100
Minutes
UF-ID:
Scantron
Instruction:
This
exam
uses
a
scantron.
Follow
the
instructions
listed
on
this
page
to
fill
out
the
scantron.
A.
Sign
your
scantron
on
the
back
at
the
bottom
in
the
white
area.
B.
Write
and
code
in
the
spaces
indicated:
1)
Name
(last
name,
first
initial,
middle
initial)
2)
UFID
Number
3)
4-digit
Section
Number
C.
Under
special
codes,
code
in
the
test
numbers
3,
2:
1
2
¢
4
5
6
7
8
9
0
1
¢
3
4
5
6
7
8
9
0
D.
At
the
top
right
of
your
scantron,
fill
in
the
Test
Form
Code
as
B
.
A
e
C
D
E
E.
This
exam
consists
of
14
multiple
choice
questions
and
4
{ree
response
questions.
Make
sure
you
check
for
errors
in
the
number
of
questions
your
exam
contains.
F.
The
time
allowed
is
100
minutes.
G.
WHEN
YOU
ARE
FINISHED:
1)
Before
turning
in
your
test
check
for
transcribing
errors.
Any
mistakes
you
leave
in
are
there
to
stay!
2)
You
must
turn
in
your
scantron
to
your
proctor.
Be
prepared
to
show
your
GatorID
with
a
legible
signature.
Calculus
I:
MAC2311
Exam
3
B
-
Page
2
of
14
11/14/2023
It
is
vour
responsibility
to
ensure
that
vour
test
has
18
questions.
If
it
does
not,
show
it
to
your
proctor
immediately.
You
will
not
be
permitted
to
make
up
any
problems
omitted
from
your
test
after
the
testing
period
ends.
There
are
a
total
of
105
points
available
on
this
exam.
Part
I
Instructions:
14
multiple
choice
questions.
Complete
the
scantron
sheet
provided
with
your
information
and
fill
in
the
appropriate
spaces
to
answer
your
questions.
Only
the
answer
on
the
scant-
ron
sheet
will
be
graded.
Each
problem
is
worth
five
(5)
points
for
a
total
of
70
points
on
Part
I.
Fov)
=y
=
3%
1.
Computc
dy
using
the
function
y
=
3z%
as
x
gocs
from
1
to
0.9.
X,
¥2
(A)
0.3
(B)
-0.3
(C)
0.6
(E)
none
of
the
above.
Oy
410
ar
cb
-
(QXX
(
Yo-X1)
-
LD
N
-
2.
Find
the
linearization,
L(2),
of
f(z)
=
vz
+
1
at
a
=
3.
(A)
4+
52
-3)
(B)4—
5(z—3)
(C)
2+
§(z
-
3)
LX)
L_(X)
L
(X)
(D)
2+
3(z
—3)
(E)
none
of
the
above.
=
jc(cx\-k
jC'(a\cx,a\
|
"
-
fa@)
Ffe
(x-3)
féx\‘zm
9
¥
}L1
(x-3)
70'@7
-
’L‘T{
(l
Calculus
I:
MAC2311
Exam
3
B
-
Page
3
of
14
11/14/2023
Need
Fra0=0
or
3.
Find
the
critical
numbers
of
f(x)
=
ot
(2
-
x).
h
.
A
Donaiv:
(20,00
Pl
undefine
(A)z=0
(B)z
=1
(D)z=2
(E)z=0,2
2
Jr
=
2%
(2o
+XFE0
proanet
nte)
+r0)
=
X%
(509
-
%)
%-—-51)(
:l__,%
=
O
J'(K\:
____...-—é—/-:’""—
L’\,’1¥¢O
X
-
v
Feod
andefned
oX
4.
Let
g(z)
=
2*
—
822
Let
M
be
the
absolute
maximum
of
g(z)
on
(L,
3]
and
m
be
the
absolute
minimum
of
g(z)
on
[1,
3].
Calculate
AL
+
m.
(A)
~10
(B)
-9
(C)
-8
(E)
—6
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Calculus
I:
MAC2311
Exam
3
B
-
Page
4
of
14
11/14/2023
5.
Which
of
the
following
functons
has
neither
an
absolute
maximum
nor
an
absolute
minimum
on
its
domain?
(A)
y
=
sin(z)
C)y=
Ve
(D)
y
=
a*
(E)
y
=
|2
=
X
——7
3
Has
1O
absu'm
mflk\c
(Mlfl—
|
¥
2
6.
Find
the
value
of
¢
implied
by
Rolle’s
Theorem
for
f(z)
=
(22
—
4z)3
on
[0,4].
(A)
c=0
(B)c—1
©@e=1
o
o™
Calculus
I:
MAC2311
Exam
3
B
-
Page
5
of
14
11/14/2023
7.
Suppose
that
f(z)
is
a
function
that
is
continuous
and
differentable
for
all
z.
Further
suppose
f(1)
=
=3
and
f/(z)
<
3
for
all
values
of
z.
Find
the
largest
possible
value
of
f(8).
(4)
16
(€)
20
(D)
22
(E)
24
65
MVT
5—(33*94‘_'3
=
§'CL§
fi)(SOVY’\@
Ce(/)‘?)
3z
-
|
We
IKhow
-P‘Cc\
<
3,
JCC?D’C’Z’\
=
freo
5(8\1»
TN
-3
27073
(1]
8.
Find
the
interval(s)
where
f(z)
=
2*
—
122
+
1
is
increasing.
M
'y
6(
jc
I
X)
-0
(A)
(—o0,-2)
(B)
(2,00)
(C)
(=2,2)
U
(2,00)
e
(D)
(=2,2)
(E)
(=00,
=2)
U
(2,00)
v
Te
S
re
Jry
=
2¢°-
'Z;y
"
Calculus
I:
MAC2311
Exam
3
B
-
Page
6
of 14
11/14/2023
9.
Suppose
f(z)
=
—a—
On
which
of
the
following
intervals
would
f(z)
satisfy
all
the
conditions
of
the
Mean
Value
The01
em'7
(A)
[-3.0]
(B)
[~2,2]
(©)
[0,2]
(E)
none
of
the
above.
wWe
need
F)
4o
be
con
hnwdd
on
[a,b]
.
-+
{()(\
IS
ng(:
(,(mhhl/tous
at
X
\\:6,'37
pvords
X=
T2
10.
Which
of
the
followiug
correctly
describes
f(x)
=
&3
—
222
+
27
|
JabVe
(A)
f(x)
has
two
local
maxima
and
one
local
minimum.
u
§L
f?
/\Sk
d
en
v
’
(B)
f(z)
has
one
local
maximum
W
‘,/C\S"'
’
(C)
f(z)
has
two
local
maxima
and
two
local
minima.
S"'
(D)
f(z)
has
one
local
maximum
and
two
local
minima.
M
re
.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Calculus
I:
MAC2311
Exam
3
B
-
Page
7
of
14
11/14/2023
11.
Let
f(z)
=
cos(z)
—
sin
(z).
Determine
the
interval(s)
on
[0,
27]
where
f(z)
is
concave
up
(4
0.
HUE
)
(©)
10,50
(.
21]
(D)
(.2
x
1)
=
—sin)
(,os(x)/—lmm
Y\/;‘/"‘Oa_lo
-p”(x\‘
—CJOSLX\-’rSm()()
=
O
S
()
=
S
(X
@
&,
@
1"’
]
+antd
=
|
DL(
\%
@)
‘59
e
L
T
Whe
re
is
TS
e’
C.C
¢
.C
C(;Srwh
_
T
5T
AW
up
X
)
{1’
,,.
W
O\
;Z
'
s
ol
12.
Evaluate
lim
eoloe
o
6—
UR
P
z—0
222
(4)0
(B)
3
(D)
—3
(B)
-
;Z
“M
{X_,/
te
O
vV
:
X
/
f(um
€
-
|
Calculus
I:
MAC2311
Exam
3
B
-
Page
8
of 14
11/14/2023
1
|
i
‘
h,,e
13.
Evaluate
lim
,_l+
n
()
§)
GZ
nfi’)(
’
=1
1+
cos(mx)
(4)
—3=
(B)
1
©€)
-7
(D)
%
(E)
0
'Y
14.
Given
two
numbers
whose
difference
is
50,
what
is
their
minimum
possible
product?
s,
(4)
0
(B)
—500
7(,8,*—60
—
X>‘50+‘2/
P
=
XW
[
rninim
i
Ee)
P
P-(s0ty)y
=
50474
(D)
—850
-
95
(-25)
Calculus
I:
MAC2311
Exam
3
B
-
Page
9
of 14
11/14/2023
Calculus
I:
MAC2311
Name:
Fall
2023
Exam
3
B
Section:
11/14/2023
Time
Limit:
100
Minutes
UF-1ID:
Part
II
Instructions:
4
frce
responsc
questions.
Neatly
give
a
complete
solution
to
cach
problem
and
show
all
work
and
intermediate
steps.
We
are
grading
the
work
and
notation
as
well
as
the
answer.
A
total
of
35
points
is
possible
on
Part
II.
The
first
three
questions
are
worth
7
points
and
the
final
question
is
worth
14.
No
credit
will
given
without
proper
work.
If
we
cannot
read
it
and
follow
it,
you
will
receive
no
credit
for
the
problem.
For
Instructor
Use
Only:
FR
1
FR
2
FR
3
FR
4
Total
Points
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Calculus
I:
MAC2311
Exam
3
B
-
Page
10
of
14
11/14/2023
1.
Clearly
state
the
indeterminate
form
of
the limit
helow.
After
this,
evalnate
the
limit,
stating
the
use
of
L’
Hopital’s
rule
wherever
applicable.
radung
Jim
(7
+
2)¢
Calculus
I:
MAC2311
Exam
3
B
-
Pagell
of
14
11/14/2023
2.
Find
the
absolute
maximum
and
minimum
of
f(z)
=
%%
on
the
interval
[—5,
5].
Find
(nhcal
H5
n
[’515]‘
Prdy
=
(xea)
(20
|-
(20|
b
|2
J
9=
=
T
TN
Jo)
=
(=1
abs
)
T1e
)
O:ongOZ
L?g
=
(X
c+
x0¢C
.
og
+
X817
XC
Q)/f
Q
ASHre)
T
A
=
(I
f
(\O
ER‘L’Z!\M!\JQ\M
f.g
M?Wl
‘U310
Y3
03
9895012
st
Jry)
¢
+
xg
=
fi
aur]
ay)
uo
Jwod
9y}
pui
‘¢
(007
/
£e0e/v1/11
p1Jo
gl
9%ed
-
¢
¢
wexy
TTECOVIN
‘1
su[nore)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Calculus
I:
MAC2311
Exam
3
B
-
Page
13
of
14
11/14/2023
4.
Let
f(z)
=
m'li(z
-
5).
Part
1.
List
the
function’s
domain,
intercepts,
and
vertical
or
horizontal
asymptotes.
DUW\OL'\V\
=,
o)
\V\‘\'fir%{"rs
B
(O\O\)
(5)03
[
T
YB(S|jME1'D"CS
T
NoNe
Part
2.
Use
the
first
derivative
to
find
the
intervals
where
the
function
is
increasing/decreasing.
Also
give
the
x
valucs
at
which
any
local
maxima
or
minima
occur
and
their
corresponding
y-valucs.
425
Crdeal
=
:
f,(m)_@
Lrex>=0
—a
Uy-<=20
{100
unsechied
(P\mes/‘?osi
ke
)
@
@
)
¢Qoreasiw%
:
(—90,03
v
(o,
%
\
locol
mun:
(=
_-H.0)
=
N
BN
<>
NN
i
>
e
e
s
&l
)
&
g
Part
3.
Find
the
intervals
where
the
function
is
concave
up/concave
down
and
points
of
inflection.
2(2z
+5)
f"(x\‘—o
-
o(ax+s)=0
LoD
u,..\gujiine.e)
A=
¥
o+
\¥X=0
)
(oncane
up
.
(-02,7%)
v(o>)
5
Concanesoun
=
(772
2)
nhecnsn
ponts
©
(%
20,
Lo
o)
G
Using
the
earlier
parts,
sketch
the
graph
of
f(x)
=
3
(z
—
5)
on
the
next
page.
Calculus
I:
MAC2311
Exam
3
B
-
Page
14
of
14
11/14/2023