Bc Practice Examination 1 Worksheet Page 10
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10612
AP Calculus
Part B
TIME:
60 MINUTES
4 PROBLEMS
No
calculator is allowedfor any
of
these problems.
If
you finish Part
B
before time
has
expired,
you
may
return to work on Part
A,
but you
may not
use a
calculator.
3.
The
velocity
of an
object
in motion in the plane for 0 :S
t:S
1
is
given
by
the vector
(a)
When
is this
object at
rest?
(b) If
this
object
was
at the origin when t
=
0,
what are
its
speed and position when
t
=
I?
(c) Find an equation of
the
curve
the
object
follows,
expressing
y as
a function of x.
4.
(a) Write the
Maclaurin
series (including
the general
term) forf(x)
=
!n(e
+
x).
(b)
What
is the radius of convergence?
(c)
Use the first three
terms
ofthat
series
to write an expression
that estimates
the
value of
f
In(e
+
x
2
)dx.
5. After pollution-abatement
efforts,
conservation
researchers
introduce 100 trout into a
small
lake. The researchers
predict that after
m
months
the rate of
growth, F,
of
the
trout population will
be
modeled
by the
differential equation
dF
=
0.0002F(600
- F).
dm
(a) How
large
is
the trout population when it
is growing
the
fastest?
(b) Solve
the
differential
equation,
expressing F
as a
function of m.
(c) How long after the lake was stocked will the population be growing the fastest?
6.
(a)
A spherical snowball
melts
so that
its
surface area
shrinks
at
the
constant
rate
of
10
square centimeters
per
minute.
What
is
the
rate
of change
of
volume when the
snowball
is 12 centimeters
in
diameter?
(b)
The snowball
is
packed most
densely
nearest the
center.
Suppose
that,
when it
is
12
centimeters
in
diameter, its density
x
centimeters
from
the
center
is
given
1
by d(x)
=
-f;,
grams per
cubic
centimeter.
Set up an integral for the total
1+
x
number
of
grams
(mass) of the snowball
then.
Do not evaluate .
•
END
OF
TEST
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