Math 2574 Calculus III
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First Exam (solutions)
6 Jun 2014
In a nal answer, a scalar expression (whether numeric or algebraic) does not need to be simplied, even if
it is a
Cal III , Quiz 11, Fall 12 Feldman
Name :
StudentID# :
Section time :
Consider the cone z 2 = x2 + y 2 for 0 z 1 (i.e, the sides of the ice cream cone) for
both of the following problems.
1. Use your
36
31 1
The density of thorium. which has the FCC structure and one atom per lattice
point, is 11.72 g/cm3. The atomic weight of thorium is 232 g/mol. Calculate
(a) the lattice parameter; and
(b) the
46
413
BCC lithium has a lattice parameter of 3.5089 X 103 cm and contains one
vacancy per 200 unit cells. Calculate
(a) the number of vacancies per cubic centimeter; and
(h) the density of Li.
Soluti
324 Detemline the indices for the directions in the cubic unit cell shown in
Figure 334.
Solution: A;o,o,1 1,0,0=1,0,1 = [l01]
B: 13,145,141 = J/ZL1=[121
C:1,0,00,=1=l,,-1=[4l
D:0,1,)g1,0,0=1,1,)=[21]
J v M 77 m/
/"f Section time :
Evaluate the line integral fer the k . ,
5' = yi + 3:23 (i.e., f F . Tds). WOT 1n 30mg from (1: 0) t0 (0, 3) under the force
V'Jc- fr: +(f NJ/ (alzmjfln235r-f) _/f_-Z/:
Math 2574 Calculus III
NAME:
(Please print clearly)
Fourth Exam (solutions)
16 July 2014
1. Evaluate the following line integrals. In both cases C is the curve with parametrization
r(t) = 3 sin t, 2 3
Math 2574 Calculus III
NAME:
(Please print clearly)
Third Exam (solutions)
2 Jul 2014
1
1
1
dx dy.
+1
y
0
(a) shade the region of integration in the gure below and
(b) evaluate the integral by rst rev
Math 2574 Calculus III
NAME:
(Please print clearly)
Second Exam (solutions)
19 Jun 2014
1. Find the indicated partial derivatives.
(a) For w =
Ans:
w w
w
sin(xy 2 )
, nd
,
, and
.
3xy + z
x y
z
w
y 2
Cal III , Exam 4 , Fall 12 Feldman Name :
Show all your work.
Set up means all limits included and no clot products or cross products in integral.
StudentID# :
Section time :
1. Find f (a: y)ds for th