RULES

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RULES
Arithmetic sequence:
Tn= a+(n-1) d
general term

Sn= [2a + (n-1) d]


Sn= [a+l]

0>a+(n-1) d
when order first negative term.
Geometric sequence:
Tn= arn-1
Sn=
S∞=
general term
( −)
−

−
Matrices & determinists:

(
−

)

Row
Column
Order= Row × Column 2×2
‫ومتتغباش ر‬
‫وتضب هم ف بعض هما كدا شكلهم حلو‬
1

A= (

−
)

 
- At= (
)
− 
 −
- 2A= (
)
 

- A2 = A × A = (

- (
[( × ) + (− × )]
[( × ) + ( × )]



|


|




|
−

)×(


−
) = Row × Column

[( × −) + (− × )]
)
[( × −) + ( × )]
= [(2×6) -(1×5)] = 12-5 = 7


| = 2|




| -1 |




| +7 |



|=

Using Cramer’s rule to solve it:
- X+2Y=4

Δ=|


Δx= |


Δy = |

X=
Y=




=
=
&
2X+Y=5

| = (1×1) -(2×3) =-3


| = (4×1) -(2×5) = -6


| = (1×5) -(4×2) = -3

−
−
−
−
=2
=1
2
If A= (



Δ=|


) find A-1 (multiplicative inverse of A)


| = 30


 
A-1 (
 −
 
−
)= (
 −

−
−

) = (−


)


Diffraction:
Y = F(x) ----->


1- If Y = axn -----→
2- If Y= a
3- If Y=

5-
6- Y=



=0

----→ Y= 3 (2x-5) ---→
4- F1×F2 ----→
√ 
= nxaxn-1

a≠0 ----→





(F1) × F2 + F1 ×
 
 
-----→
----→
=



− -6
x


=

−


(F2)




( )× − × ( )
= 
7- Y= [F(x)] n ------→



( )
= n[F(x)] n-1 ×


F(x)
3
‫‪Integration:‬‬
‫‪+c‬‬
‫‬
‫‪+c‬‬
‫‪+c‬‬
‫‪−‬‬
‫‪−‬‬
‫‬
‫‬
‫‬
‫‪+‬‬
‫= ‪1- ∫  dx‬‬
‫‬
‫‬
‫= ‪2- ∫ √ dx = ∫  dx‬‬
‫‬
‫= ‪3- ∫  dx = ∫ − dx‬‬
‫‬
‫‪∫  dx = 3x+c‬‬
‫‪4- ∫  dx = ax+c‬‬
‫‪+c‬‬
‫‪+c‬‬
‫‪+‬‬
‫‬
‫‪(+)+‬‬
‫×)‪(+‬‬
‫‪[()]+‬‬
‫‪+‬‬
‫= ‪5- ∫( + ) dx‬‬
‫‬
‫= ‪6- ∫[()] F(x) dx‬‬
‫‬
‫‪Ex:‬‬
‫ ) ‪∫ ( −‬‬
‫‬
‫ ) ‪= ∫ ( −‬‬
‫‬
‫‪+c‬‬
‫‬
‫]‪[ −‬‬
‫‬
‫‬
‫=‬
‫الشخص الذي ميكنه أن يكون أي شخص ويصنع أي شيء سوف يتعرض للنقد والذم وإساءة الفهم‪،‬‬
‫هذا جزء من مثن العظمة‪.‬‬
‫‪4‬‬
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