S08 Math 1205 -- Test 2 24 Mar 2008 NAME:
Justify all work using complete sentences ! Use only methods from class.
1.[8]
lim
h
Ø0
I2+
h
M2+1-5
h
is the difference quotient for a function at
x
=2
. What is the function? (Do NOT evaluate the limit)
2.[8] Find the equation of the tangent line to
f
H
x
L=
x
2+2
x
at
x
=1
.
3.[32] Find the derivative of the following functions:
a)
h
H
x
L=1-
x
2
b)
f
H
x
L=cosI
x
3M
x
c)
g
H
x
L= ‰sin2H
x
L
d)
f
H
x
L=I3
x
2+7M
1
x
4.[16] Find the appropriate derivative.
a) Find
„
y
„
x
if
tan-1H
y
L=xy
b) Find
„2
y
„
x
2
if
3
x
2+6
y
2=2
5.[8] Suppose
h
is given by
h
H
x
L=
f
I
g
2H
x
LM
with known values:
x f
H
x
L
f
' H
x
L
g
H
x
L
g
' H
x
L
-1-5 4 -1-3
1-1-2 1 7
Determine the value of
h
' H1L
if possible. SHOW WORK.
6.[10]
f
H
x
L=:
x
2+2
x
+1
x
§1
2
x
2
x
>1
a) What is the right-hand derivative of
f
H
x
L
at
x
=1
?
b) What is the left-hand derivative of
f
H
x
L
at
x
=1
?
c) What is
f
' H1L
?
7.[10] A rocket that is launched vertically is tracked by a radar station located on the ground 3 miles from the launch site.
What is the vertical speed of the rocket at the instant that its distance from the radar station is 5 miles and this distance is
increasing at the rate of 4000 miles per hour?
8.[8] Suppose that the velocity of a particle along a straight line is given in the left graph below. Assuming that
s
H0L=0
, draw
the graph of the position over the same interval on the right axes.
1 2 3 4 5 6
t
-2
-1
1
2
vHtL
1 2 3 4 5 6
t
-2
-1
1
2
sHtL
