MAT 305 Review for Test 1 1. Important Definitions: groups, subgroups, subroup lattice, order of an element, Abelian groups, order of a group, Euler phi-function, cyclic groups, generators of cyclic groups, permutations, groups of permutations, odd e
shah (njs2463) HW01 beshaj (54030)
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001
10.0 points
Evaluate the integral
Z e
I =
2x ln(x) dx .
1
1. I =
1 2
(e 1)
shah (njs2463) HW02 beshaj (54030)
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001
10.0 points
Find the value of the integral
Z 5
2
dx .
I =
2
3 4 + (x 3)
1.
shah (njs2463) HW3 shih (56235)
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001 10.0 points
A heavily loaded freight train moves with
constant velocity.
What
Version 033 Test 1 pavlovic (53515)
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001
Determine if
lim
10.0 points
002
1
10.0 points
If the function f is conti
shah (njs2463) HW1 shih (56235)
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001 (part 1 of 2) 10.0 points
A rope has a cross section A = 9.3 m2 and
density =
shah (njs2463) HW03 beshaj (54030)
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1
so that
lim It = lim
t
t
1
2
1
1
= .
2(4t + 1)
2
Consequently, the integral
shah (njs2463) HW2 shih (56235)
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001 (part 1 of 2) 10.0 points
While following the directions on a treasure
map, a
RL Voltage
Voltage across black resistor
current across black
0.06
0.006
0.057
0.0057
0.0579
0.00579
0.0603
0.00603
0.0583
0.00583
0.0598
0.00598
0.0639
0.00639
5.72
4.96
4.42
3
1.5
0.02
0.26
0.007
0.006
0.005
0.004
0.003
I
V
0
0.006
0.0057
0.00579
0.0060
MAT 305 Fall'07 Test 1
SHOW ALL YOUR WORK TO GET PARTIAL CREDIT.
1. Find the order of each element in the indicated group: (a) 6 in Z15 (b) ( 2 7 3 )( 1 2 4 ) in S8 , (c) 11 in U(14) and 2. Let G = <a> be a cyclic group with order |G| = 15 (a) List
MAT 305 Review for Test 2 1. Important definitions: Rings, integral domains, fields, units, zero divisors, characteristic of a ring, ring homomorphism, ring isomorphism, ideals, prime ideals, maximal ideals, principal ideals, quotient ring, ring of p
MAT 305 Test 2
Fall'07
I. List all the units and in each case find its multiplicative inverse in : (a) Z8 , (b) Z [i] , (c) Z7[x] , (d) Q( 2)
II. Find all the zero divisors ( if any ) in : (a) Z7[x] , (b) Z6[x] , (c) Z2 x Z3 , (d) Z [i]
III. Find
Version 087 Test 2 pavlovic (53515)
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001
10
9
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
If
f (x) = 4x2 + 3x ,
which of the