FINAL EXAMINATION
-
MATH
141
INSTRUCTIONS:
1.
Substantiate
all
answers.
2.
Work
only
one
problem
on
each
answer
sheet.
You
may
use
both sides
of
the
answer
sheet
for
the
same
problem.
3.
At
the
top
of
each
answer
sheet,
write
(a)
your
name,
(b)
your
section
number,
(c)
your
TA's
name,
and
(d)
the
problem
number.
4.
Hand
in
all
answer
sheets
(properly
filled out),
even
if
you
do
not
work
on
some
problems.
5.
No
audio
devices
are
allowed;
no
calculators
are
allowed
unless
explicitly
approved
by
your
professor.
xarcsinx
(10)
1.
a.
Evaluate
lim
โ-โโโโ
.
x->o
X
2
+
sm
x
)
Evaluate
tan
"
3/2
x
sec
4
x
dx.
(10)
f
1
1
(10)
c.
Determine
whether
I
โโโ
-
dx
converges.
Give
reasons.
Jo
(x-1)
2
(10)
/I.
a.
Let
f(x)
=
x
5
+
3x.
Explain
why
f
has
an
inverse,
and
find
(f'
l
)'(-4).
(15)
b.
Evaluate
\
*
+
dx.
J
x
2
-9
(15)
3.
a.
Evaluate
jtsec
2
5tdt.
/
f
gX
(10)
J&
Evaluate
โโ
โ
dx.
*
J
2x
(15)
4/
t
Evaluate
(10)
tf.
a.
Write
an
integral
for
the
volume
V
of
the
solid
generated
by
revolving
โข
about
the
x
axis
the
bounded region
between
the
graphs
of
y
=
8
-
x
2
y
=
x
2
.
Do
not
evaluate
the
integral.
(15)
b.
Find
the
length
L
of
the
curve
given
paramctrically
by
x
=
1+
-
t
3
and
y
=
-
t
2
for
0
<
t
<
1
