math 200 final review
I the 6x 47 12 intersects X-axis , y-axis,
the
plane
=
.
+
3y +
and z-axis in points P, Q ,
and R respectively find the area of the
ofPAR
triangle
1 .
5) find the plane that is parallel to the plane 4x-5y + z =
2
which contains (4 , 0 ,
-1) .
2 evaluate
SSp(Fxy) &A R 20 , 2] x(0 , 13
=
.
sevaluate So Y
dx
dy
4let Xty2
f(x ,y) =
,
find maxtmin values w/ the
constraint 2x2+ ya = 2
b)x find global maxt min over the
region
D
G(x y)/2x2 y2124
=
, +
5 let .
f(x , y) In)1 + X + 2y)
=
·
find of (u , 1) /2 21
a =
,
where X =
1 + 1 12 + and
y
=
cos(20-12)
6 .
let Fit =< t3-1) 1-t32t> , ,
find
length
traced over the bounded
0xt = 1
curre
by
, 1 the 6x 47 12 intersects the X-axis , y-axis,
plane
=
.
+
3y +
and z-axis in points P, Q ,
and R respectively find the area of the
ofPAR PR
triangle A 11 BX ACI
=
6X =
12
T5 = -
AB 2
,
4 , 07
X= 2 -
AR (2 , 0 %
=
,
AC =
c
-
2 0
, ,
33
12
5122 + 62 + 82
3y =
11 AB X All
y 4 =
=H
BX (0 , 4 , 0
t22
=
=
z 3 =
-
203
CR 10 , 0 , 3)
=
i(12 0) j) - - -
b -
0) k(0 8)+ +
12i +
6j + 8k
< 12
,
6 , 87
find the plane that is parallel to the plane(X-5y +z =
2
which contains (4 , 0 ,
-1) . normal rector
- of the plane
= 5 , 1)
-
is coefficent
4(x 4) 5(y 0) + 1(z + 1)
- - - = 0
4X 16 - -
5y + 0 + z +1 = 0
4x
5y + z 15
-
=
.
2 evaluate
SSp(#xy) &A R 20 , 2] x(0 , 13
=
Solo (ixydy) dy u =
1 + xy
du = dy
Sils
*
+
2
-
ul
Sol-x
18 x -
In (1 + x)
2- 1n3
I the 6x 47 12 intersects X-axis , y-axis,
the
plane
=
.
+
3y +
and z-axis in points P, Q ,
and R respectively find the area of the
ofPAR
triangle
1 .
5) find the plane that is parallel to the plane 4x-5y + z =
2
which contains (4 , 0 ,
-1) .
2 evaluate
SSp(Fxy) &A R 20 , 2] x(0 , 13
=
.
sevaluate So Y
dx
dy
4let Xty2
f(x ,y) =
,
find maxtmin values w/ the
constraint 2x2+ ya = 2
b)x find global maxt min over the
region
D
G(x y)/2x2 y2124
=
, +
5 let .
f(x , y) In)1 + X + 2y)
=
·
find of (u , 1) /2 21
a =
,
where X =
1 + 1 12 + and
y
=
cos(20-12)
6 .
let Fit =< t3-1) 1-t32t> , ,
find
length
traced over the bounded
0xt = 1
curre
by
, 1 the 6x 47 12 intersects the X-axis , y-axis,
plane
=
.
+
3y +
and z-axis in points P, Q ,
and R respectively find the area of the
ofPAR PR
triangle A 11 BX ACI
=
6X =
12
T5 = -
AB 2
,
4 , 07
X= 2 -
AR (2 , 0 %
=
,
AC =
c
-
2 0
, ,
33
12
5122 + 62 + 82
3y =
11 AB X All
y 4 =
=H
BX (0 , 4 , 0
t22
=
=
z 3 =
-
203
CR 10 , 0 , 3)
=
i(12 0) j) - - -
b -
0) k(0 8)+ +
12i +
6j + 8k
< 12
,
6 , 87
find the plane that is parallel to the plane(X-5y +z =
2
which contains (4 , 0 ,
-1) . normal rector
- of the plane
= 5 , 1)
-
is coefficent
4(x 4) 5(y 0) + 1(z + 1)
- - - = 0
4X 16 - -
5y + 0 + z +1 = 0
4x
5y + z 15
-
=
.
2 evaluate
SSp(#xy) &A R 20 , 2] x(0 , 13
=
Solo (ixydy) dy u =
1 + xy
du = dy
Sils
*
+
2
-
ul
Sol-x
18 x -
In (1 + x)
2- 1n3
