Chapter 10 Test
April 8, 2008
No Calculators
Name
1. Find the equation of the normal line to the curve if
x
=
sin
2
t,
y
=
cos2
t
where
t
=
7
p
ÄÄÄÄÄÄÄÄ
6
2. If
x
=
e

t
and y
=
e
2
t
,
then find
d
2
y
ÄÄÄÄÄÄÄÄÄÄÄÄ
dx
2
in terms of
t, and discuss the concavity of this plane curve for
 • <
t
< •
3. Find the length of the curve if
x
=
ln
H
cost
L
,
y
=
t ,
and
0
£
t
£
p
ÄÄÄÄ
3
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4. Solve the initial value problem
dr
ÄÄÄÄÄÄÄ
dt
=
H
cot
2
t
L
i
+
i
k
j
j
j
j
j
1
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
ÄÄÄÄÄÄ
2
t
è!!!!!!!!!!!!!!
t
2

1
y
{
z
z
z
z
z
j
where
r
H
1
L
=
<
0, 1
>
5. Find the unit vectors
H
four in all
L
that are tangent and normal to
x
=
7
t

t
3
,
y
=
1
+
t
2

5
t,
at
t
=
1
6. Find the slope of the tangent line for
r
=
1

sin
q
, at
q =
p
ÄÄÄÄ
2
.
7. Sketch the graph of the polar equation, and be sure to label at least three polar points
H
r,
q
L
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