Elementarna Matematika - Mehmed Zehra Nurkanović - skraćeni pregled

Embed Size (px)

Citation preview

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    1/30

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    2/30

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    3/30

    Prof. dr. sc. Mehmed Nurkanovi}Doc. dr. sc. Zehra Nurkanovi}ELEMENTARNA MATEMATIKA - Teorija i zadaciRecenzenti:

    Dr. sc. [efka Arslanagi}, vanredni profesorPrirodno-matemati~ki fakultet Univerziteta u SarajevuDr. sc. Hasan Jamak, vanredni profesor

    Prirodno-matemati~ki fakultet Univerziteta u Sarajevu

    Izdava~:PrintCom, d.o.o., grafi~ki in`enjering, Tuzla

    Za izdava~a:Jasmin Had`imehmedovi}

    Korektura, kompjuterska obrada teksta i naslovna strana:AUTORICrte`i:

    Dr. sc. Zehra Nurkanovi}, docent

    [tampa:PrintCom, d.o.o., grafi~ki in`enjering, Tuzla

    Za {tampariju:Delila Had`imehmedovi}

    Tira`:500 primjeraka

    CIP - Katalogizacija u publikacijiUniverzitetska i narodna biblioteka

    Bosne i Hercegovine

    Strogo je zabranjeno svako umno`avanje i pre{tampavanje ove knjige bez saglasnosti au-tori. Neovla{teno kopiranje, umno`avanje i pre{tampavanje predstavlja krivi~no djelo iz~lana 100. Zakona o autorskom pravu (Sl. list RBiH br. 2/92 i 13/94).

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    4/30

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    5/30

    #%" " *"&"

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    6/30

    #$"("$

    D4DP39 41 >1 >1O5= CAQG9OCD B;?A? 41 9 >5=1 =1C5=1C9Q3;98 ;>:971 D ;?:9=1B5 >1 B9BC5=1CB;9 >1Q39> ?2A1ID:D >1:E1QG>9:9 49:539@9A1>5 C1;? 41 >1 B1=?= @?Q35C;DB14AQG5 >1:29C>9:5 C5?A5CB;5 @?BC1E;5 DG 2?71CD 95 D;5OC? C5QG5 G141C;5 ;?:9 BD 95;9= =1C5=1C9Q3;9=>1C:531>:9=1 9:1 1 >1;?> C?71 B:1 D@DC5 9 A5GD:98?E98 A:5O5>:1 4?21A =5C?49Q3;9 @A9BCD@ :5A :5 >1

    :2? E9O5 @?;DO1:1 41 5E5>CD1? @?7:5 D@DCD 91;?> C?71 @A9BCD@5 9GA149 G141C1;1 G1 B1=?BC1 A14 C5 41 @A9 C?=5 BE?:5 A5GDDI5>9= A:5O5>:9=1 D 4AD7?= @?7CA?:D @?:549>98 G141C1;1 %1 C1:

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    7/30

    !=:4*78>2D, ) !=:4*78>2D,

    >1Q39> ?>9 P35 B5 @?BC5@5>? ?B@?B?2:5 ;1;? BC1>41A4>98 C1;? 9 C5QG98 @A?25 =1C5=1C9;5 1 9BC?EA5=5>? P35 DB1EAO1E1C9

    @?BCD@1; G1 C1;E? A:5O1E1>:5 + ?;E9AD CA9>15BC5 B5;39:5 @AE?7 @?7 G1 @A?35>C>9 A1Q3D> ?21C1 :?O ?4 ?B>?E>5O;?D @1QG>:D 2D4DP39 41 @A1;B1 @?;1GD:5 41 DQ35>939 >54?E?? 4?2A? E9= 61;D9 9B@9C9 >1+>9E5AG9C5CD D *DG:98 B14AQG1>9 BD G14139 D C?;D @?B:5 CA9O;?5 B1 C5BC?E1 9G @A54=5C1 C1A>1 11 &4B:5;D $1C5=1C9;1'A9A?4>?=1C5=1C9Q3;?7 61;D?7?=5 @?=?P39 BCD45>C9=1 D @A9@A5=1=1 G1 @?:5 9B@9C19G ?E?7 @A54=5C1 BC1;>9=? 41 @A541E1>:1 9G ?E?7 @A54=5C1 D7?= @A1C5B14AQG1: @A5C8?4>98 B5;39:1 @AE?7 @?7:975 :5OC? B14AQG9 C5?A9:B;D 1>1:1 A1G>98 :54>14QG29 9>5:54>14QG29 5C1A>5 =1C5=1C9;5 B @1A1=5CA9=1 @A?21DC;1 7?4 ;141 B5 ?E1:

    9B@9C DC5=5BCE5> 9B@9C G1 79=>1G9:5 >1 C5A9C?A9:9 *DGB;?7 ;1>C?>1%1 C1: >1Q39> DQ35>939=1 B5 @ADQG1 9GDG5C>1 @A99 @A57:98 G1:54>9Q3;98 =1CDAB;98 9B@9C1 1:97D D @D>?=;1@139C5CD =?7D EA

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    8/30

    %*-:E?*3

    &.8:23* 2 ?*-*,2 #8527862 $*,287*57. /=74,23. 27.*:7. 3.-7*-E?+. %2;*-:**-:*5 6D>;39:5

    "E14A1C>5 :54>14QG25 9 >5:54>14QG25 ;BCA5= 9 C?; ;E14A1C>5 6D>;39:5 ,9SC5?E5 6?A=D15 :54>14QG25 A139?>15 >5:54>14QG25

    4;987.7,23*57* /=74,23*4;987.7,23*57. 3.-7*-E?+. 2 7.3.-7*-E?+.

    80*:2

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    9/30

    !=:4*78>2D, ) !=:4*78>2D,

    7*52?=B;9 61;D

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    10/30

    5.6.65:54>14QG25

    '?:1= ?=5CA9:1 9>?=>9 ?2A1G13 A9C=5C9Q3;9 9 75?=5CA9:B;9 >9G

    A9C=5C9Q3;9 >9G 5?=5CA9:B;9 >9G

    '9=5CA9:1 >1

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    11/30

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    12/30

    #805*>53.

    &.8:23* 2 ?*-*,2

    #8527862

    .@72,23* A;8067. 5 9G ?4A5I5>98

    A1G9 DE9:5; =?7D B=1CA1C9 @??=9=1 :54>5 @A?=:5>1 @? ? ?4>?B>? ;1?@??= Q35CEAC?7 BC5@5>1 @? ) 91 @? *

    )1Q31:>5 @A1;C9Q3>5 @?=?P39 @A9 A:5O1E1>:D >5;98@A?2

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    13/30

    !=:4*78>2D, ) !=:4*78>2D,

    / -/6> ?B65 8

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    14/30

    5.6.65;14 :5 @?CA52>? ?4A549C9 B1=? ?BC1C1; @A9 49:5:D 4E1:D @??=1 @A9Q35=D >1B ;?9; D?@P35 >5 G1>9=1 + B9= 29>?=?= ? ? C?=5 7?E?A9 B

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    15/30

    !=:4*78>2D, ) !=:4*78>2D,

    #:263.: &1>216@6 B>6721;

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    16/30

    5.6.6

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    17/30

    !=:4*78>2D, ) !=:4*78>2D,

    &@P35>9C? C? 9G79 CA9>?= ?29C9 @A1E9

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    18/30

    5.6.6?BC 9GA1G1

    ? ? ? ?

    (1BC1E9C9 >1 @A?BC5 61;C?A5

    ? @ A ? @ A

    ? @ A ?@A

    ? ? ? ?

    ?

    @

    ? @ @

    A

    A @ A

    ?

    ? A

    )* )+ *+) * + )*+

    )* + *+ ) +) * )*+

    ) * + ) * +

    ?

    ?

    ?

    @) ? ?) @ )? @

    ?@ A @A ? A? @

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    19/30

    !=:4*78>2D, ) !=:4*78>2D,

    ?;1G1C9 :54>1;?BC9

    1 ?@ ? @ ?@ ? @ ? @?

    2 ?@ A ? @A ? @ A? @ A

    ? @ A ? @ A? @ A ? @ A

    &4A549C9 ) 9 * C1;? 41 @??= ? ? ? )? * 2D45 4:59=1 ?

    %1P39 G29A ;?5H39:5>1C1 @??=1

    1 ?

    ?

    ?

    ?

    ?

    2 ? ? ? ? ? 3 ? ? ? ?

    %1P39 DE:5C5 @?4 ;?:9=1 :5 9GA1G

    ) ) )

    4:59 2A?:5E9

    '??= )? )? ) B 39:5C9=1 ) )) 4:5:57?E98 ;?5H39:5>1C19=1 4:5

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    20/30

    5.6.6

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    21/30

    !=:4*78>2D, ) !=:4*78>2D,

    )141 9=1=? (" ? ? ? ?

    / (" ? ?

    ? ? ? ?

    0 "1;? :5

    ) *

    ) *

    ) *

    ) * ) *

    ) *

    ) * ) *

    ) )* *

    ) * ) *

    ) )* *

    ) * ) * ) *

    9=1=? (" ) * ) * ) * ) )* * ) )* * *"?4 A139?>198 1? :5 E?49C9 A1Q3D>1 ? 45H>939?>?= @?

    4ADQ3:D C: B;D@D BE98 EA9:54>?BC9 @A?=:5>9A1> *D B5 @A9:5 BE571 =9B1 B1G9E>939 =?A1:D 29C9 A1GD9A1> G1 ?

    C: ? 4?; :5 9GA1G) *

    ) *45H>9A1> ;14 :5 ) * & C?: Q39>:5>939 B5 BCA?7?

    =?A1 E?49C9 A1Q3D>1 @A9 9GE?I5>:D A1GB6?A=139:1 A139?>198 9GA1G1 *1;?

    :5 :54>1;?BC ?

    ? ? C1Q3>1 B1=? D B1;?BC9 >5=1 B=9B1 9=1 'A5C8?4>1 B5:54>1;?BC =?QG5 @A?=1CA1C9 9 G45B>1 D:D A1G19= 9GA1G9=1 @?CA52>??4A549C9 45H>939?>? @?4ADQ3:5 9 BCA?7? E?49C9 A1Q3D>1 ? 9GA1G9=1 ;?:9=1 @A?O9AD:5=?9198 11BC?:9 ;A1:>:9 A5GD1@9B1C9 D?25B;A1C9E?7 A1G

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    22/30

    5.6.6

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    23/30

    !=:4*78>2D, ) !=:4*78>2D,

    #:263.: &1>216@6 B>6721;

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    24/30

    5.6.6

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    25/30

    !=:4*78>2D, ) !=:4*78>2D,

    ?

    ? @

    @

    @ ?

    ?@

    ? @

    ? @

    ?@

    ? @

    )

    ? ) )?

    )

    ? )

    ) )

    ?

    )

    )

    ) )*

    *

    ) *

    *

    )* *

    ) *

    ) *

    ? @

    ? @? @

    ? @

    0.

    @

    ?

    @

    ?

    ?

    @

    @

    ??

    @

    @

    ?

    1/

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    26/30

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    27/30

    !=:4*78>2D, ) !=:4*78>2D,

    ;? :5 ) * + 4?;1G1C9 41 EA9:549

    ) *+

    * +

    )

    + )

    *

    +

    ) *

    )

    * +

    *

    + )

    %5;1 :5)

    *

    *

    + ?;1G1C9 41 :5 C141

    )*+

    )

    *

    +

    ) * +

    ?;1G1C9 41 1;? :5 ) ? EA9:549)

    ?

    ?

    )

    ? )

    )?

    ;? :5 ) * + 4?;1G1C9 :54>1;?BC

    ) *

    +

    * +

    )

    + )

    * +

    ) *

    )

    * +

    *

    + ) )*+

    )

    *

    +

    &4A549C9 9 C1;? 41 G1 BE5 4?GE?5 EA9:54>?BC9 ? EA9:549 :54>1;?BC

    ?

    ? ?

    ?

    ?

    ?

    +@A?BC9C9 9GA1G

    ?

    ? @ ? A

    @

    @ A @ ?

    A

    A ? A @

    ;? :5?

    )

    @

    *

    A

    + 9

    )

    ?

    *

    @

    +

    A

    4?;1G1C9 41 EA9:549?

    )

    @

    *

    A

    +

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    28/30

    2931 *DGC1;?E9P3 -/6>8. >672H2;65 [email protected]. 6D :.@2:..@682 D. 1>A46 >.D>21 ?>21;724 A?:72>2;

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    29/30

    !=:4*78>2D, ) !=:4*78>2D,

    ./ $ %DA;1>?E9P3 - %DA;1>?E9P3 -/6>8. [email protected]. 6D :.@2:.@682 D. =>6=>2:.;72=>672:;65 6?=6@. ;. 3.8A9@2@6:. ;?>?=B;9 61;DB6 >.D>21 ?>21;765H8?EP3 $.@2:.@6?8.;@2 =>6=>2:. D. A=6?;. 3.8A9@2@ $1C5=1C9B;?@ 5?7A14

    ./ ( Q-9E;?E9P3 1C;9P3 - )CD@1A -/6>8. [email protected]. 6D :.@2:.@682 ?. >72H2;76:. A=A@.:. 6 >2DA9@.@6:. )E:5C

  • 8/9/2019 Elementarna Matematika - Mehmed Zehra Nurkanovi - skraeni pregled

    30/30