MATH 220 Final: MATH 220 Amherst S17Final Exam Final
15 Feb 2019
School
Department
Course
Professor
-Final Examination
\Iathematics
12
May,
2011
No
books,
notes,
calculators
or
communications devices
allowed.
Please
express
yourself
clearly,
and show
your
reasoning.
Thank
you.
1.
(9
points)
Evaluate each
of
the
following
integrals:
?
()
(a)
(b)
Ix
3
lnCirx
3
)dx
(c)
14
e
i.i
cosx)
-‘I
dx
2.
(8
points)
For
each
of
the
following
improper
integrals,
determine
whether
or
not
it
converges.
In
any
case
of
convergence, evaluate
the
integral.
3
1
1
(a)
f
dx
(b)
1
2
°J
9
_x2
x
—3x+2
3.
(8
points)
For
each
case
below,
determine
whether
or
not
the
limit
exists.
If
it
does,
find
its
value.
(a)
urn
—
sinh
X
(b)
urn
(1+
x2
)IflX
x—0
x2
x3
x—
4.
(8
points)
Let R
be
the
region
beneath
the
graph
of
y
=
cos
x
and
above
the
x-axis,
for
0
<x
<
(a)
[f
R
is
rotated
about
the
y-axis,
determine
the
volume
of
the
resulting
solid.
(b)
If
R
is
rotated
about
the line
y
=
—1,
determine
the
volume
of
the
resulting
solid.
5.
(9
points)
Consider
the
curve
defined by
x
=
tant
—
1,
y
ln(cos
t),
0
t
(a)
Determine
the
slope
of
this
curve
when
t
=
(b)
In
which
quadrant
does
this
curve
lie
(ignore
its
endpoints).
(c) Find
the
length
of
this
curve.
6.
(6
points)
The
curve
C
is,
by
y
=
2,
0
x
3,
is
revolved about
the x-axis.
Find
the
area
of
the
resulting
surface.
