MATH
4iO
R.
Johnson
Exam
! '
October
I
1
),
!'
You
must,
show
all
your work
to
receive
full
credit.
DO
PROBLEM
1
ON
ANSWER
SHEET
#1
(20)
J
.
Compute
the
derivative.';
of
the
following
functions
where
they
exist
(a)
f
(x)
=
---.--^
x
A
-5x +
6
(b)
,00
--3
-
1)0
PROBLEM
2
ON
ANSWER SHEET
it2
(20)
2.
Compute
the
derivatives
of
the
following
functions
(a)
f(x)
=
sin
/x~
(!>)
g(x)
-
I
.-in
2
(x'+l)
DO
PROBLEMS
.5
& 4
ON
ANSWER
SHEET
//
3
(15)
3.
Compute
the
first three
derivatives
of
f(x)
=
cos
2x
-
sin
x.
2
4
25xv
(15)
4.
Eind
the
equation
of
the line
tangent
to
the
curve
2x"~
+
3y
=
~โ~"โโ
at
DO
PROBLEMS
fi
& 6
ON
ANSWER
SHEET
//4
(15)
5.
A
rope
is
attached
to
the
bow
of
a
sail
boat
coming
in
for
the
evening.
Assume
that
the-
rope
Is
drawn over
a
pulley
7
feet
higher
than
the
bow
at
a
rate
of
2
feet
per
second.
How
fast
is the
rope
being
pulled
in
when
the
boat
is
24
feet
from
the
dock?
(15)
6.
Calculate
df
for
f(x)
=
/1+x
at
a=2
with
h
=
-0.001-
Use this
to
approximat.
f
(2-.001).
Idn:10/84