QUIZ 6
Name
1. Find both rst order partials for the function f (x, y ) = x2 y 2 sin (xy ) 3 x
2. Find all second order partials for
3. For f (x, y, z ) = e2xy
z2
y
+ xz sin (y )
z = x2 y 4x + 3 sin (y )
nd fxx and fyyzz
2
4. Compute the equation of the t
EXAM 2
Math 232
August 2, 2013
Name
1. Find the tangent plane for f (x, y ) = x3 2xy at the point (1, 1). (5 pts)
2. Find each of the following. (5 pts each)
2
(a) fx if f (x, y ) = 3ex y x 1
(b) fyxy (/2, 2) if f (x, y ) = 3x sin (y ) + 4x3 y 2
sin (x y
QUIZ 5
Name
1. Find all values of t for which the function (t) = t2 , t, t2 5 is orthogonal to (t)
r
r
1
2. Evaluate
0
2
4
, et2 , tet
t+1
dt
3. Find the position function (t) if (t) = t, 0, 16 , (0) = 12, 4, 0 and (0) = 5, 0, 2 .
r
a
v
r
QUIZ 1
Name
1. For the vectors = 3, 5, 7 and = 0, 2, 2 nd:
w
v
(a) 2 5 .
v
w
(b) | |
v
(c) + 2 .
v
w
(d) (are these two vectors orthogonal?)
vw
2. The water from a re hose exerts a force of 200 pounds on the person holding the hose. The
nozzle of the hose
QUIZ 2
Name
1. Determine whether the vectors = 4, 1, 1 and b = 2, 4, 4 are orthogonal.
a
2. Let = 1, 1, 2 and b = 1, 0, 2 . Find projb (a).
a
3. Find two vectors that are perpendicular to both = 1, 2, 1 and b = 1, 3, 1 .
a
4. A constant force of 30, 20 p
QUIZ 3
Name
1. Decide whether the line dened by x = 4 + t, y = 2 and z = 3 + 2t and the line dened by
x = 2 + 2s, y = 2s and z = 1 + 4s are parallel, skew or intersecting.
2. Find the equation of the plane containing the point (1, 1, 5) with a normal vect
QUIZ 7
Name
1. Use implicit dierentiation to nd
z
z
and
for the equation 3x2 z + 2z 3 3yz = 0
x
y
2. Find the gradient of f (x, y, z ) = z 2 e2xy 4xz 2 at the point (1, 2, 2).
3. Compute the directional derivative of f (x, y ) = xy x2 y + sin (x) cos (y )
QUIZ 8
Name
1. Show that
2xy 3
does not exist.
(x,y )(0,0) x2 + 8y 6
lim
2. Find the equation of the plane tangent to f (x, y ) = x2 + 2x + y 2 3y at (3, 0).
3. Find the direction of maximum increase for the function f (x, y, z ) = 4x2 yz 3 a the point
(1
QUIZ 14
Name
1. Find the gradient eld which corresponds to f (x, y ) = 5xy 3 3y + x cos (2y )
2. Determine whether or not the vector eld F (x, y ) =< y sin (xy ), x sin (xy ) > is conservative.
(If it is write out the potential function.)
2
ln (y )
3. Cha
QUIZ 11
Name
1
x
(x 2y )ex2y dy dx.
1. Evaluate
0
0
4x2
2
2. Evaluate
2
sin (x2 + y 2 ) dx dy . (Hint: Polar coordinates?)
0
3. Find the surface area for that portion of the surface z =
x2 + y 2 between y = x2 and y = 4.
QUIZ 13
Name
1. Find the gradient eld which corresponds to f (x, y ) = y sin (x)
2. Determine whether or not the vector eld F (x, y ) =< x 2xy, y 2 x2 > is conservative. (If
it is write out the potential function.)
3. Find the ow lines for the vector eld
QUIZ 13
Name
1
2
(3y 2 x + 4) dx dy
1. Find
0
2. Find
2x
x dA where R = cfw_(x, y ) | y 0, y
R
by y = 0 and above by y = 4 x2 )
4 x2 (That is: the region bounded below
3. Find the volume of the solid bounded by z = x2 , z = 1, = 0 and y = 2.
QUIZ 10
Name
1. Evaluate
2xy dA where R is the part of the circle, centered at the origin, of radius 4
R
which is contained in the rst quadrant.
2. Find the mass and the center of mass for the lamina with density (x, y ) = y 2 + x + 1 which
is bounded by
QUIZ 12
Name
1. Compute the volume of the solid below the curve z = 4 x2 y 2 and contained in the region
y = x, y = 0 and x = 1.
4
2
2
ex dx dy
2. Find
0
2y
EXAM 1
Math 232
July 19, 2013
Name
1. Let = 1, 1, 1 , = 2, 1, 0 and = 3, 0, 3 . Find:
v
w
c
(a) ( 2 )
v
c
w
(b)
v
w
(c) The vector of magnitude 2 that points in the same direction as .
v
(d) The angle between and .
v
w
(e) Find Comp ( ).
wv
2. A constant