mvc e assignment1
TRANSCRIPT
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MVC E1 - 1
MVC Chapter 1 EAssignment
Lines/Planes
1-1 (MVC Jun 1997 Q1) If the Vector 6,3,2 is normal to the plane through thepoint (1, 2, 3), then the equation of the plane is
1432(E)
14632(D)
1332(C)
49632(B)
1432(A)
=++
=+
=++
=+
=++
zyx
zyx
zyx
zyx
zyx
1-2 (MVC Jun 1998 Q1) If the Vector 1,2,3 is normal to the plane through the point
(2, 2, 1), then the equation of the plane is
523(E)
1423(D)
922(C)
923(B)
1122(A)
=+
=+
=+
=+
=+
zyx
zyx
zyx
zyx
zyx
1-3 (MVC Aug 2002 Q8) A plane is formed by the lines 1and2which intersect at thepoint (1, 2, 1), where
+=
+=
0,2,11,2,1,,:
1,1,21,2,1,,:
2
1
szyxl
tzyxl
The equation of this plane is
552(E)
332(D)
332(C)132(B)
152(A)
=
=+
==+
=+
zyx
zyx
zyxzyx
zyx
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MVC E1 - 2
Functions of Several Variables
1-4 (MVC Jun 1997 Q2) If yxf sin= , thenyx
f
2
is equal to
yxy
yxy
y
y
y
cossin(E)
cossin(D)
cos(C)
cos(B)
sin(A)
+
1-5 (MVC Jun 1998 Q2) If )sin(),,( xyxzzyxf += , thenyx
f
2
is equal to
)cos()sin((E)
)sin()cos((D)
)sin((C)
)sin()cos((B)
)cos((A)
2
xyxxy
xyyxy
xyxy
xyxyxy
xyyz
+
1-6 (MVC Jun 1999 Q10) If )cos(),( xyxyyxf += , thenyx
f
2
is equal to
)cos()sin(1(E)
)sin()cos(1(D))sin(1(C)
)cos((B)
)sin((A)
2
2
xyxyxy
xyxyyxy
xyy
xyyy
1-7 (MVC Jun 2000 Q2) If xyyxyxf cossin),( += , thenyx
f
2
is equal to
+
+
xy
xy
xyyx
xy
xyy
sincos(E)sincos(D)
sincos(C)
sincos(B)
sinsin(A)
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1-8 (MVC Aug 2002 Q18) If )sin(),,( xyxzzyxf = , thenzx
f
2
is equal to
abovetheofNone(E)
)sin((D))cos()sin((C)
)cos()sin((B)
)sin()cos()((A) 2
xyxxyxyxy
xyxyzxy
xyyzxxyzyx
+
+
+
Directional Derivatives
1-9 (MVC Jun 1997 Q7) Let 322 4),,( zyxzyxg += . The directional derivative of g
at (1, 2, 3) in the direction 4,3,0 is
5463
14
444
5444
5588
14588
(E)
(D)
(C)
(B)
(A)
1-10 (MVC Jun 1998 Q6) Let 222 3),,( zyxzyxf = . The directional derivative offat
(3, 2, 2) in the direction of the vector 1,2,2 is
34
34
38
2
6
38
(E)
(D)
(C)
(B)
(A)
1-11 (MVC Jun 1999 Q11) Let 23),,( zyxzyxf += . The directional derivative offat
(2, 1, 3) in the direction of the vector 2,3,1 is
63(E)
7(D)
143(C)
147(B)
3(A)
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MVC E1 - 5
1-15 (MVC Aug 2002 Q11) The cylinders in the
sketch are level surfaces of a functionf. A
formula forf(x,y,z,) could be
222
22
22
22
22
(E)
)((D)
(C)
(B)
(A)
yxz
yxz
zz
zy
yx
+
+
+
+
1-16 (MVC Feb 2006 Q1) For the surface in 3R specified by
0222 =+ zxyyx ,
a set of parametric equations for the normal line to the surface at the point (0, -1, 1)
are:
abovetheofNone(E)
,121,2(D)
,121,2(C)
,121,2(B)
,121,2(A)
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MVC E1 - 6
1-18 (MVC Jun 1998 Q7) The tangent plane to the surface 6=xyz at the point
)1,2,3( is
63(E)
6632(D)
18632(C)
1423(B)
1938(A)
=+
=+
=
=
=+
zyx
zyx
zyx
zyx
zyx
1-19 (MVC Jun 1999 Q12 & Q13) Q12 & Q13 refer to the function 1),,( 2 += yxzzyxf .
Q12 : A normal to the level surface f= 0 at (1, 2, -3) is
1,4,3(E)
3,4,1(D)
3,2,1(C)
1,2,3(B)1,1,3(A)
Q13 : The plane tangent tof= 0 at (1, 2, -3) has equation
43(E)
1834(D)
1432(C)
243(B)
223(A)
=
=+
=+
=
=
zyx
zyx
zyx
zyx
zyx
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MVC E1 - 7
1-20 (MVC Jun 2000 Q4 & Q5) Q4 & Q5 refer to the level surface 1232 22 = zyx .
Q4 : A normal to the level surface at the point (2, 1, 2) is
2,3,2(E)
2,3,2(D)
2,6,8(C)
2,6,8(B)
2,1,2(A)
Q5 : The equation of the plane tangent to the level surface at (2, 1, 2) is
3232(E)
334(D)1334(C)
3232(B)
922(A)
=++
==++
=
=++
zyx
zyxzyx
zyx
zyx
1-21 (MVC Aug 2002 Q20 & Q21) Q20 & Q21 refer to the function xyzzyxf =),,(
Q20 : A normal to the level surfacef = 6 at (3, 2, 1) is
2,3,6(E)
3,6,2(D)
6,3,2(C)
1,1,2(B)
1,2,3(A)
Q21 : The plane tangent to f = 6 at (3, 2, 1) is
=++
=++
=++
=++
=++
18632(E)
92(D)1423(C)
26236(B)
21362(A)
zyx
zyxzyx
zyx
zyx