2. Set up,but do not eval
uate, a triple integral in cylindrical coordinates for
the volume above the pl
anez=1 andinsidex2+y2+22=5.
V: gff%\/
l) '1. J37;
_; cfw_my cfw_VA%AV A49
0 O l
3. The soli
Math 241 Quiz 8: Problems 1, 2, and 3 are worth 2, 3, and 3 points.
1. Set up, but do not evaluate, a double integral for the area inside of one
pedal of the 3pedaled rose 1" = 25in 36.
I L<(~\3L9'
:
Math 241 Quiz 1: All problem's are worth 2 points.
1. Find the equation of the plane that contains the point (1, 2, 3) and that
is perpendicular to the line a: = 1 375, y = 5t, z = 7 + 4t.
3L1A\3+ a (
Math 241 uiz 2: .
Q thee, A a.\ cum/(C.
1. True or False (1 point each) - L, (K \L - ' la,
1" (a) If ( )lim( b) f(a:, y) = L for all lines l in the xyplane passing
93,9 ~41 a,
through (1,6), then (
Math"24l Quiz 5: Each part of problem is worth 2\points
1. Consider the 2dcontour map of
f(x, y) aketched on the right. Given
. that the maximumrate of change
at the point P is 2, sketch Vf(P).
2. (
.- _ - -
Math 241 Quiz 3: Each pfoblem is worth 2 points,
1. For a unit vector 21' = (a, b), state the denition of D3 f (m, y).
D4 cfw_Lw j: QM, OOH-k tLD - FOR \
a J 14 8 b k
2. Given that f(x, y, z)
4 . . 4
j: Math 241 Quiz 14: Each Problem is worth 2 points.
1. Based on the diagram below, is [C F dn positive, negative, or 0? Note:
F 15 tangent to C.
2. Based on the diagram below, is [a H dn
Math 241 Quiz 7: Each problem is worth 2 points x (:\
1. Set up (specify the limits) the double integral
D / xzy dA relative to the order of
integration dA : dmdy. Do not evaluate.
Math 241 Quiz 9: Problems 1, 2, and 3 are worth 2, 3, and 3 points.
1. A solid bounded in the rst octant by z = 9
Setup, but do not evaluate,
a:2 y2 has density 6 = myz.
a triple integral for the mass
_,. . -
Math 142 Quiz 15: Each part of each problem is worth 2 points.
1. State the product rule -for curl (ff).
Cuval: K 5r C.QVcfw_(:
2. (a) Using the partial derivative test, verify that the vector
Math 241 Quiz 6: Problems 1, 2, and 3 are worth 2, 3, and 3 points.
1. The 2dcontour representation of f (:13, y)
and the level curve g(:v, y) = 3 are sketched
on the right. What is the absolute minim
Math 241 Quiz 13: Each problem is worth 2 points.
1. Based on the diagram, is / F - df positive, negative, or 0? Note: The
. C . _.
circle C is oriented counterclockwise and F is tangent to C.
3. De
'Math 241 Quiz 12: Each part of each problem is worth 2 points.
1. For the trajectory t) 2 (cos 2t, t, sin 2t), determine
(a) the unit tangent vector T.
'3 l ~ ~ _ .
)- v : <r~Lman l, 1L be .
T V \I
.- . . a- . -| a-
Math 241 Quiz 11: Each part of each problem is worth 2 points.
1. Sketch in 3d.
2. Set up, but do NOT evaluate, a triple integral in spherical coordinates for
the volume bounded ab
Math 241. Quiz ;4: Each problem is worth 2 points.
1. Find the differential df where f(a:, y, z) = 2:23 + yz.
M = mm a at; _+ a aa
2 52541 & 23 oKj + Exizcixi
2. Find the rate of change of the functi