it 2012.pdf · polynomial using array + 2x + lists write function to delete an element from dll....
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( ) ~ ~p q p p q� � � �
( ) ( ) ( )p q r q r p r r� � � � � � �
R .A {1, 2, 3, 4}�
2 2 2 2 (2 1) (2 1)1 3 5 ....... (2 1)
3
n n nn
� �� � � � � �
1 1 0 1 0 0
H 0 1 1 0 1 0
1 0 1 0 0 1
� �
� � �
(A B) (A B)�
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No.
2(D 3D 2)xey e� � �
22 2
2(2 3) (2 3) 2 24
d y dyx x y x
dx dx� � � � �
21 , | | 1
0, | | 1
x x
x
� � ���
��
30
cos sinx x x
x
�� � �� �� cos
2
xdx
1L E sin ,
C
dii dt pt
dt� ��
,dq
id t
� � 2 1
LCp �
1F ( ) , | | 3
( 3)( 4)z z
z z� �
� �
2
2F( )
1
zz
z�
�
�
�
4
�
· 0a r
r
�� �� � �� �
4 2
2
6( log )r r
r� �
2 2F ( cos ) (2 sin )y x z i y x j� � �
(2 )xz k� �
F � ��
� �
F. dr�
F
, 1,2 2
� �� � �� �
F
S
F . ,n ds��
2 ˆˆ ˆF ( 1)xi yj z k� � � �
S
ˆ( F). ,n ds� ���
F k̂
�C F . dr F [ sin ]xe y y� �
[ (1 cos )]xe x y j� �2 2
2 21, 0
x yz
a b� � �
S
ˆˆ ˆ ˆ( ). S,yzi zxj xyk n d� ���
� ��E2
4� � � � � �
S V
E . 4 Vds d� � � ��� ���
3
2
C
3 5 2
( 2)
z zdz
z
� ����
2 2
19 25
x y� �
2
C
3
2 5
zdz
z z
�� ���
,1 1
2 3
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3 21x x� � �
7 4 3M( )x x x x x� � � �
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15 0 0 22 0 15
0 11 3 0 0 0
0 0 0 6 0 0
0 0 0 0 0 0
91 0 0 0 0 0
0 0 28 0 0 0
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