MAC2312
Prof Howard 3-16
Summer 2007
Test 3
Name
1. Set up but do not evaluate.
Find the arc length of the curve I(x) = x - sinhx for x E [0,1].
L
~~ .£1 .H\-~x)'-
~
dx
2. Set up but do not evaluate.
\1
'I
Find the area of the surface obtained by rotating the curve f(x)
x E 0, 7r
[ 4]
<Jt-::
l
.
= secx
tic. X)::
~¥,
J-::-
)
Y. -= ~("
Secx
~)C
+L~)=
+(secx~x) dx
_I \
( ""ij)
(OS
~
+\(~):: ~~.\1..
OL
.I~
3. Set up but do not evaluate.
Findthe arc lengthforthe curve
x= et
. where t E[0,7r].
Y = sm!
~
=
Ccs,
~~
-~j
0*-
Find the area of the ~~on enclosed by r
A
::
= sin2B.
5o ~ ( S,'(\2B) 1.d&
.R-
eJ(-
~
4. Set up but do not evaluate.
y
u--<-"
about the x axis for
L
J rr See-X
o
cp 5'I-
-=
-
-I
~;z..
£..
.
5. GIven
x
X
= 2cost -/-~
y = sin2t
a. Eliminate the parameter to find the Cartesian equation.
X"111
'"
;J
~S ~V\1=
.J-
::: tJ (0 '!>1.
::
'X'1.",,"a.J'I
=::. L./
b. Sketch the curve and indicate with an arrow the direction of the curve.
6.
(A)
Match the following parametric equations with their graphs.
x =- sin t
y
= t - cost
(B)
= sin 3t
y = sin 4t
X
(C)
x =t 3 - t
Y = t2 -1
@
Ji
7. Find the equation of the tangent line to the curve x
y
::;
~
X=e
~
I
I)
V\1~
~ _ \
\
:=D
for t
= 1.
0
-
4>-~'
~
( e
::=e
=
e
= t - lnt
::
D
(x-e)
~\
'i WI
~ the appropriate graph.
8. Match the equation
(A)
r
= 1+ 4cos(5B)
(B)
r
= sinB+
(C)
r = sin(8B/ 5)
sin3(5B/2)
@
9. Given (x - 3)2 + (y + lY
4
a. Find the cente..
16
=1
C.(3)-1)
V ( 3) 3') (3.J -~)
c. Find the foci.
f (
3J
- I -t~f.3)
10. Given (x- 2)2 =8(Y~
a. Findthe vertex. / \.J
b. Findthefocus./
(
f (,/-H)
- \)
~)
F ( 2) \)
'/ f --3
- --
- ~ -
.
ed
ed....
11. GIven r = 1 :J:ecos B and r = 1 :J:esm
. B determme which IS an elhpse, parabola, and
hyperbola.
r=
r=
r=
10
3- 2cosB
-
J
6
1+ 2sinB
6
1- smB
. e ;:: :2/:3
lD/3
==
)
-
_I&,
-:.)
o
LeL
I
coe
.
-
)
e::::l
e. "/ I
I .,.. J51ftB
--
to
\ - IS
',It
e
)
e
}
e
::= I
(
\
hpe{Po
pczrQbo{Ct