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21 2014

( 21 2014) (0,5 ). 7 .

4 :

1. Word 1 - 4 ( : Eponymo.Onoma-GE2.doc).

, . ,

Excel

.

2. Excel Excel (

: Eponymo.Onoma-GE2.xls). Excel

Excel.

. .. 3-, 4 .

. 13

.

Excel Excel. T word.

(Equation Editor) Word ( : Insert Object Object type Microsoft Equation 3.0 :

Microsoft Equation 3.0).

(Equation Editor)

.

CD Microsoft Office. Equation

Editor / (. 68-71), 13

(http://class.eap.gr/deo13) :

Egxeiridio H-Y.pdf.

1 [20 (5+5+5+5)]

[ ] (15 (5+5+5)) : QP 35,152 =

: QQQVC 175155,0 23 +=

300=FC .

() TC, TR . (5 )

() Q . (5 )

() MC R. Q

. ; (5 )

[ ] (5 ) 3 3,30 . 2000 . :

1) 5,0= .

2) 1= .

3) 2= .

(5 )

1 -

[ ]

()

:

TC= VC+FC= 321 Q -15Q2+175Q+300

:

TR= PQ=(152,5-3Q)Q=152,5 Q - 3Q2

:

=TR-TC=152,5Q-3Q2-( 321 Q -15Q2+175Q+300)= - 3

21 Q +12Q2-22,5Q - 300

()

1

= 5,222423 2 + QQ

2

= 2432426

+=+ QQ

=0 5,222423 2 + QQ =0 Q=15 Q=1

=0 2

Q=1 (1)=-3*1+24=21>0 .

Q=15 (15)=-3*15+24=-21

: MR C Q* . : (Q)=TR(Q)-TC(Q),

(Q)=TR(Q)-TC(Q)=MR(Q)-MC(Q) Q*

(Q*)=0.

[ ]

Q1=2000 P1=3.

TR1=P1 x Q1=3x2000=6000.

H PdPQdQ

PQ //

, =112

112

/)(/)(PPPQQQ

=

1) 5,0= 3/)330,3(

2000/)2000(5,0 2

=

Q

1900)05,0(200020002000

200010,0)5,0( 22 =+=

= QQ

TR2=P2 x Q2=3,30x1900=6270 .

: 10%

10%

.

2) 1= 3/)330,3(

2000/)2000(1 2

=

Q

1800)10,0(200020002000

200010,0)1( 22 =+=

= QQ

TR2=P2 x Q2=3,30x1800=5940 .

: 10%

10% .

3) 2= 3/)330,3(

2000/)2000(2 2

=

Q

1600)20,0(200020002000

200010,0)2( 22 =+=

= QQ

TR2=P2 x Q2=3,30x1600=5280 .

: 10%

10% .

2 [25 (3+5+5+7+5)]

962 ++= QQPs

25102 += QQPd .

() Ps, Pd Excel Q 0 6,5

0,25. Q . (3

)

() Ps Pd Ps>0 Ps , Pd>0 Pd . (5 )

() . (5 )

() Pd Q 10%. (7 ) (E) (). (5 )

(:

( Q P ),

,

.

Q.)

2 -

()

Q Ps Pd 0 9 25

0,25 10,5625 22,5625 0,5 12,25 20,25

0,75 14,0625 18,0625 1 16 16

1,25 18,0625 14,0625 1,5 20,25 12,25

1,75 22,5625 10,5625 2 25 9

2,25 27,5625 7,5625 2,5 30,25 6,25

2,75 33,0625 5,0625 3 36 4

3,25 39,0625 3,0625 3,5 42,25 2,25

3,75 45,5625 1,5625 4 49 1

4,25 52,5625 0,5625 4,5 56,25 0,25

4,75 60,0625 0,0625 5 64 0

5,25 68,0625 0,0625 5,5 72,25 0,25

5,75 76,5625 0,5625 6 81 1

6,25 85,5625 1,5625 6,5 90,25 2,25

P

A B

C

Q

()

Q

. : (i) 0Q , (ii) 0>sP

0>dP (iii) , 0'sP

, 0'dP .

(i) (ii)

1 . (ii), 22 )3(96 +=++= QQQPs 0>sP 0Q . ,

22 )5(2510 =+= QQQPd 0>dP

5Q . (i) (ii) 0Q 5Q .

(iii) : Ps Ps=2Q+6 0Q

0'sP .

Pd Pd=2Q-10. 0'dP 50102 QQ .

, (i),

(ii) (iii) 50

()

Ps Pd Ps = Pd Q=1.

.

Ps = Pd Q2+6Q+9 = Q2-10Q+25 6Q+9 = -10Q+2516Q= 16Q=1

Q=1 = 12+6*1+9=16

()

Q 10% 10 =Q 10,11 =Q .

10,11 =Q 21,1525)10,1(1010,12

1, =+=dP

( : 05,0049375,016/)1621,15(/)( 0,0,1, == ddd PPP .

dP 5%.)

. ( ,

.)

Pd (

) (Q=1,

P=16)

2510102

2510)102( 2

2

2 +

=+

==QQ

QQQQ

QQPQ

dQdP

d

dd

Q=1 5,016

825110111012

2

2

=

=+

=d

Q 10% Pd

(0,5x10)%=5%.

:

. (dy/dx)

y/x=(y2-y1)/(x2-x1).

()

Q=1 :

33,202521)10(

31]25

210

3[)2510( 10

2321

0=+=+=+ Q

QQdQQQ

:

=20,33-(1x16)=4,33

(1x16)= =Q x P.

3 [25 (6+6+6+7)]

MR : 216100)( QQQMR += Q . ,

23650)( QQQMC += .

, () 0=FC

.

.

() N TC, AC. (6 )

() N TR Pd ( Q) . (6 )

() N Q

. (6 )

() N Q . EXCEL,

TC, TR,

Q 0 13 0,5. (7 )

3

()

TC TR MC MR :

++=+== CQQQdQQQdQQMCTC3

32

650)3650()(32

2 .

:

00)0(0 === CTCFC . QQQTC 503 23 += .

5032 +== QQQ

TCAC

()

:

++=+== cQQQdQQQdQQMRTR32

16100)16100()(32

2 00)0( == cTR .

32

318100 QQQTR += .

QPTR = , (

) . ,

232

318100)3/1(8100 QQP

QQQQ

QTRP dd +=

+== .

()

: )503(1008)3/1( 2323 QQQQQQTCTR +++== .

QQQ 5011)3/4( 23 ++=

0ddQ

= 2

2 0ddQ

< .

20 50 22 4 0d Q QdQ

= + =

Q1 = 7,23 Q2 = -1,73. ,

Q1 = 7,23 Q2 = -1,73 . ,

Q1 = 7,23 :

084,35)23,7(82282222

4 [30 (8+6+6+5+5)]

) :

1) 752

)( += xexf

2) 423 )75(2)( += xxxf

3) )75ln()( 2 += xxf

4) 3253

)21()4()(

xxxf+

=

(8 ) B) :

(5) 10)25()( = xxf

(6) )25(

1)(

=x

xf

(7) )25()( = xexf

(: ) (6 )

) :

8) + dxexx x)52( 2

9) dxxx )ln( (: ) (6 )

) :

10) 4

0)2( dxxx

11)

1

20)

313( dxxe x

(5 ) ) :

12) 4432)( 234 ++= xxxxxf ,

(5 ) 4)

1) u=5x2+7 y=eu .

dxdu

dudy

dxdy

= = 752

)10(10 += xu exxe

2) . u=5x2+7 z=2x3 y=z u-4 .

22 632)'( xxdxdzz ===

)10()75(4)52()4()()()'( 52544

4 xxxudxdu

duud

dxudu

+==== .

:

=+= )'()()'( 44 uzuzdxdy )10]()75(4)[2()75)(6( 523422 xxxxx +++ =

= 5224

52

422

52

4

42

2

)75(4250

)75(80)75(6

)75(80

)75(6

++

=+

+=

+

+ xxx

xxxx

xx

xx .

3) u=5x2+7 y=ln(u).

dxdu

dudy

dxdy

= =75

10)10(1 2 +=

xxx

u

4)

62225332243

)21()4()21(3)4()21(3)4(5

xxxxxxx

dxdy

++

=

42

3243

)21()]4)(4()21(5[3)4(

xxxxxx

++

= 42343

)21(]1656[)4(3

xxxxx

+++

=

4) 5) u=5x-2

dxu 10

dx du du=d(5x-2)=5dx dx=51 du .

dxu 10 = CxCuduu +=+= 55

)25(115

151 111110

6) u=5x-2

dxu1

dx du du=d(5x-2)=5dx dx=51 du .

dxu1 = cxcudu

u+=+= 25ln5

1ln511

51

7) u=5x-2

ceceduedxe xuuu +=+== 2551

51

51

4) 8)

( )2 2 5 xx x e dx + =

( ) ( )2 2 5 2 1x xe x x x e dx = + +

( ) ( ) 11 1x x x x x x xx e d xe x e d xxe e e c xe c = + = + + = +

( )2 2 5 xx x e dx + = ( ) ( )2 22 5 2 5x x xe x x xe c e x c + + = + +

9)

2 2 2 2 2 1ln ln ln ln2 2 2 2 2x x x x xxlnxdx xd x d x x dx

x= = = =

2 2 2 21 1 1ln ln ln2 2 2 2 2 2 2x x x xx xdx x c x c = = + = +

4) 10)

==

== 2/32/5

4

0

2/32/54

0

2/12/34

04

344

52

2/32

2/5)2()2( xxdxxxdxxx

1532

152523

324

52)4(

34)4(

52 563632/152/1 ====

11)

)20ln(31)(3|]20|ln|1|[ln

31][31

313)

313( 201201

1

20

1

20

1

20+===

eeeedxxdxedxxex

x

4) 12)

4432)( 234 ++= xxxxxf

:

3 2( ) 4 6 6 4f x x x x = +

:

=+++=+=+ )1(6)1)(1(4)1(6)1(44664 2323 xxxxxxxxxxx

)252)(1(2]3)1(2)[1(2 22 ++=+++ xxxxxxx

-2, 12

1.

:

( ) ( )2 212 12 6 6 2 2 1f x x x x x = + = +

-2, 12

1:

( )2 18 0f = > -2 .

( ) ( ) ( ) ( )4 3 2( 2 ) 2 2 2 3 2 4 2 4f = + + = 0

1 9 02

f = 1 .

04)1(4)1(3)1(2)1()1( 234 =++=f .

: : -13