Math 324 H Quiz 6
1. Let S be the part of the surface given by the equation 2x + 4y + z = 4
in the rst octant oriented away from the origin (with all components of the
normal positive). Compute the ux
Math 324 H Quiz 1 Solution
Find the volume of the solid formed in the rst octant bounded by the
planes x = 0, z = 0, x y = 0, and 3x + 3y + z = 18 inside the cylinder
x2 + y 2 = 1.
x=0
y=x
2
2
x + y =
Math 324 H (Ward)
Midterm 2 (50 Minutes)
November 22, 2013
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Instructions.
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Math 324 H (Ward)
Midterm 2 (50 Minutes)
November 22, 2013
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Instructions.
(1) Write your name on the line provided below these instructions.
(2) Your so
Math 324 H (Ward)
Midterm 1 (50 Minutes)
October 18, 2013
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Instructions.
(1) Write your name on the line provided below these instructions.
(2) Your sol
Math 324 H (Ward)
Midterm 1 (50 Minutes)
October 18, 2013
DO NOT TURN THIS PAGE UNTIL INSTRUCTED TO BEGIN!
Instructions.
(1) Write your name on the line provided below these instructions.
(2) Your sol
Math 324 H Sample Quiz Solution
Use the fundamental theorem of line integrals to compute
F dr
C
where C is the curve starting at (0, 0, 0) travelling along the x-axis to (2, 0, 0)
and then along the s
Math 324 H Sample Quiz
Use the fundamental theorem of line integrals to compute
F dr
C
where C is the curve starting at (0, 0, 0) travelling along the x-axis to (2, 0, 0)
and then along the straight l
Name:
Math 324G
Winter 2017
MIDTERM - 1
1/27/2017
Instructions: The exam is 7 pages long, including this title page. The number of points each
problem is worth is listed after the problem number. The
Math 324 H Quiz 2
Use a triple integral to nd the volume of the solid inside z 2 = x2 + y 2
between z = 1 and z = 2.
Idea: The surface z =
coordinates: z = r.
x2 + y 2 becomes the familiar cone in cyl
Math 324 H Quiz 3
Suppose f (r, ) is a function in polar coordinates. Recall that we can
convert this to rectangular coordinates using formulas r(x, y ) and (x, y ).
Part (a) Write down the multivaria
Math 324 H Quiz 4
1. Compute the directional derivative Du f at (1, 0) where u = 0, 1 and
f (x, y ) = xy + y 2 .
2. Is this the maximum value of Dv f for all unit vectors v (You must
justify your answ
Math 324 H Quiz 3
Suppose f (r, ) is a function in polar coordinates. Recall that we can
convert this to rectangular coordinates using formulas r(x, y ) and (x, y ).
Part (a) Write down the multivaria
Math 324 H Quiz 1
Find the volume of the solid formed in the rst octant bounded by the
planes x = 0, z = 0, x y = 0, and 3x + 3y + z = 18 inside the cylinder
x2 + y 2 = 1.
Math 324 H Quiz 6 Solution
1. Let S be the part of the surface given by the equation 2x + 4y + z = 4
in the rst octant oriented away from the origin (with all components of the
normal positive). Compu
Math 324 H Quiz 5
1. Compute the integral
F dr
C
where
r(t) = cos(t), sin(t)
on [0, 2 ]
x2
F(x, y ) = x sin(e ) + 2y, 3x + ey .
2
Apply Greens Theorem: P (x, y ) = x sin(ex ) + 2y and Q(x, y ) = 3x +
Math 324 H Quiz 4 Solution
1. Compute the directional derivative Du f at (1, 0) where u = 0, 1 and
f (x, y ) = xy + y 2 .
f = y , x + 2y
Du f (1, 0) = 0, 1 0, 1 = 1
2. Is this the maximum value of Dv
Name:
Math 324G
Winter 2017
MIDTERM - 2
2/17/2017
Instructions: The exam has 5 questions. The number of points each problem is worth is listed
after the problem number. The exam totals to 25 points. F