Calc Midterm 3
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Rutgers University *
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Course
151
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
6
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RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
QUIZ
©
2020
Suppose
that
the
functions
f
and
g
and
their
derivatives
with
respect
to
x
satisfy
the
following:
f(1)=0,f(2)=
-7,'(1)=7,1'(2)=3,
9(1)=3,9(2)=2,9'(1)=3,9'(2)=5
Rutgers
Quiz
(ver.
a162t)
©
2020
For
each
of
the
following functions,
compute
the
desired
derivatives.
Your
answers
do
not
need
to
be
simplified.
(a)
For
the
function
F(x)=
e
9x=
1)g(x), the
value
of
F'(1)=
9+3+
3.
Rutgers
Quiz
(ver.
a162t)
©
2020
N
(b)
For
the
function
G(x)
SIN0)
e
value
of
G
1)
!
or
the
tunction
X)=—"7-
,
the
value
0
=3
g(x)
3
Rutgers
Quiz
(ver.
a162t)
©
2020
_
)
20343423
(c)
For
the
function
H(x)=
In
([g(x)]?
+f(2
x)),
the
value
of
H
'(1)=
ST
Rutgers
Quiz
(ver.
a162t)
©
2020
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
QUIZ
©
2020
Question
is
complete.
Tap
on
the red
indicators
to
see
incorrect
answers.
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
QUIZ
©
2020
Find
the
x-coordinate(s)
of
the
point(s)
on the
curve
y =
X3
+4x%
-
2x
+
19
where
the
tangent
line
is
parallel
to
the
line
y =
—
7x
+
15.
(If
you
find
more
than
one
x-coordinate,
separate
the
numbers
by
commas.)
Rutgers
Quiz
(ver.
e745t)
©
2020
N
5
The
x-coordinate(s)
is/are:
-
30
1
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
QUIZ
©
2020
Question
is
complete.
Tap
on
the red
indicators
to
see
incorrect
answers.
RUTGERS
UNIV.
OFFICIAL
MIDTERM
QUIZ
©
2020
Suppose f(x)=b*
and
f'(0)=16.
Find
b.
b=e*.
Rutgers
Quiz
(vers.
d469r)
RUTGERS
UNIV.
OFFICIAL
MIDTERM
QUIZ
©
2020
Question
is
complete.
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RUTGERS
UNIV.
OFFICIAL
MIDTERM
QUIZ
©
2020
Consider
the
curve
with
equation
2x
e ¥
+
sin
~
1
(5y)=2.
Rutgers
Quiz
(ver.
e898r)
d
(a)
Use
implicit
differentiation
to
find
_y_
Your
answer
does
not
need
to
be
simplified.
dx
dy
24/1-25y
eV
X
f1-252
V45
Rutgers
Quiz
(ver.
e898r)
(b)
Find
an
equation
of
the
tangent
line
to
the
curve
at
the
point
(1,0).
Put
the
equation
for
the
tangent
line
in
the
box.
-
.2_
1
y=-Z(x-1)
Rutgers
Quiz
(ver.
e898r)
RUTGERS
UNIV.
OFFICIAL
MIDTERM
QUIZ
©
2020
Question
is
complete.
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
QUIZ
©
2020
Water
is
flowing
into
a
conical
tank
with
base
radius
9
ft
and
height
54
ft.
The
tank
is
oriented
so
the
the
tip
of
the
cone
is
pointed
downward.
Recall
that
the
volume
V
of
a
right
circular
cone
is
given
by
1
V=3
?h,
where
r
is
the
base
radius
of
the
cone
and
h
is
the
height
of
the
cone.
Use
this
information
in
parts
(a)
and
(b).
Rutgers
Quiz
(vers.
d217p)
©
2020
Rutgers
Quiz
(vers.
d217p)
©
2020
(a)
Find
a
formula
for
the
volume
V
of
the
water
in
the
tank
as
a
function
of
h
only,
where
h
represents
the
depth
of
the
water
in
the
tank.
You
do
not
need
to
simplify
your
answer.
Al
Ve
ta
2
2h3
=
3"
54
i
(b)
If
water
is
flowing
into
the
tank
at
a
rate
of
14
cubic
feet
per
minute,
how
fast
is
the
depth
of
the
water
changing
when
the
depth
is
45 feet?
Give
an
exact
answer
and
NOT
a
decimal
approximation.
You
do
not
need
to
simplify
your
answer.
Rutgers
Quiz
(vers.
d217p)
©
2020
hl
2.14
3,
.
>
ft*/min.
The
depth
of
the
water
is
changing
at
a
rate
of
2
ne9”
«45
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
QUIZ
©
2020
Question
is
complete.
Tap
on
the red
indicators
to
see
incorrect
answers.
@
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
©
2020
Fill
in
the
blanks.
The
figure
below
shows
the
velocity
v
=
f(t)
of
a
particle
moving
on
a
horizontal
coordinate
line
for
the
time
interval
0
<
t
<
10
seconds.
Rutgers
Quiz
(ver.
c818r)
©
2020
Velocity
as
a
Function
of
Time
Vv
Q
6_
44
=
29
o
\
/\‘
0
T
T
Y
4
6
8
10
24
-4
-6~
Rutgers
Quiz
(ver.
c818r)
©
2020
Question
is
complete.
Tap
on
the red
indicators
to
see
incorrect
answers.
Answer
the
following
questions
concerning
the
movement
of
the
particle.
For
each
answer,
type
an
equation
or
a
compound
inequality,
using
t
as
the
variable.
Use
a
comma
to
separate
answers
as
needed.
The
inequalities
and
solutions,
if
there
are
multiple,
should
be
ordered
from
left
to
right.
Rutgers
Quiz
(ver.
c818r)
©
2020
(a)
When
is
the
particle
moving
to
the right?
0<t<1,8<t<10
(b)
When
is
the
particle
stationary
for
more
than
an
instant?
1<t<?2
Rutgers
Quiz
(ver.
c818r)
©
2020
(c)
When
is
the
particle
moving
at
its
greatest
speed?
4<t<6
(d)
When
is
the
particle's
acceleration
positive?
6<t<g
Rutgers
Quiz
(ver.
c818r)
©
2020
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