מתמטיקה - 4 יח"ל - כיתה י"ב - חלק א'

ﺟﺑﺭ ﻭﻣﻘﺩّﻣﺔ ﻟﻠﺗّﺣﻠﻳﻝ ﺍﻟﺭّﻳﺎﺿﻲ ﻟﻠﺩّﻭﺍﻝ ﺍﻷﺳّﻳّﺔ ﻭﺍﻟﻠّﻭﻏﺭﻳﺛﻣﻳّﺔ

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ﺍﻟﻔﺻﻝ :8 ﺗﺣﻭﻳﻼﺕ ﻋﻠﻰ ﺍﻟﺩّﺍﻟّﺔ ﺍﻟﻠّﻭﻏﺭﻳﺛﻣﻳّﺔ

أﺟﻮﺑﺔ ﻧﮫﺎﺋﯿّﺔ

y

(1) )ﺃ( ) i ( ﺍِﻧﻌﻜﺎﺱ ﺑﺎﻟﻨّﺴﺒﺔ ﻟﻠﻤﺤﻮﺭ x . ) ii ( ( ) f x : 0

( ) f x

x 

x  ، ( ) g x : 0

( ) ln g x x 

x 

)ﺝ( 0

)ﺏ(

x

1

)ﺩ( ﺍُﻧﻈﺮﻭﺍ ﺍﻟﺮّﺳﻢ ﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﺴﺮﻯ

( ) ln g x x  

( ) g x

(2) )ﺃ(

1

)ﺏ( x  . )ﺝ( ﺇﺯﺍﺣﺔ ﻋﻤﻮﺩﻳّﺔ ﺇﻟﻰ ﺍﻷﻋﻠﻰ ﺑﻮﺣﺪﺓ ﻭﺍﺣﺪﺓ . )ﺩ( ( ) g x – ﺭﺳﻢ ﺑﻴﺎﻧﻲ I ، ( ) f x – ﺭﺳﻢ ﺑﻴﺎﻧﻲ II . )ﻫـ( ) i ( 1 0 ( , ) ) ii ( 1 0 , e _ i )ﻭ( 0 x  ْﻥ ﻫﻮ ◌ْ ﻣﺠﺎﻝ ﺗﻌﺮﻳﻒ ﺍﻟﺪّﺍﻟّﺘَﻲ 0

x 

x  ، ( ) g x : 0

(3) )ﺃ(

( ) f x : 0

y

( ) g x

)ﺏ( ﻛﻼّ .  )ﻫـ( ﺍِﻧﻌﻜﺎﺱ ﺑﺎﻟﻨّﺴﺒﺔ ﻟﻠﻤﺤﻮﺭ y ﻭﺍﻧﻜﻤﺎﺵ ﻋﻤﻮﺩﻱ ﺑـ 4 ﺃﺿﻌﺎﻑ ) ﺗﻤﺪّﺩ ﺑـ 0.25 ﺿﻌﻒ(. )ﻭ( ﺍﻧﻜﻤﺎﺵ ﻋﻤﻮﺩﻱ ﺑـ 4 ﺃﺿﻌﺎﻑ ) ﺗﻤﺪّﺩ ﺑـ 0.25 ﺿﻌﻒ(. )ﺯ( ﺍُﻧﻈﺮﻭﺍ ﺍﻟﺮ ﺳﻢ. )ﺡ( (3) ﻋﻠﻰ ﺍﻟﻤﺤﻮﺭ x . )ﺝ( 0 x  )ﺩ( 0.25 ( ) ln( ) x h x 

( ) f x

( ) h x

1 1 

x

1 0 ( , ) 

x 

x 

)ﺩ( ﺭﺳﻢ ﺑﻴﺎﻧﻲ I .

)ﺝ( 0

)ﺏ(

(4) )ﺃ(

0

)ﻫـ( ) i ( ﺇﺯﺍﺣﺔ ﻋﻤﻮﺩﻳّﺔ ﺇﻟﻰ ﺍﻷﺳﻔﻞ 5 ﻭﺣﺪﺍﺕ .

) ii ( ﻛﻼّ .

x 

)ﺡ(

)ﺯ(

)ﻭ( 0

y

y

( )

g x

( ) h x

x

x

(5) )ﺃ(

( ) f x – ﺭﺳﻢ ﺑﻴﺎﻧﻲ II ، ( ) g x – ﺭﺳﻢ ﺑﻴﺎﻧﻲ I ، ( ) h x – ﺭﺳﻢ ﺑﻴﺎﻧﻲ III . )ﺏ(

A 2 0 ( , )

)ﺝ( ﺗﻤﺪّﺩ ﻋﻤﻮﺩﻱ ﺑﻀﻌﻔَﻴْﻦ . )ﺩ( ﺍِﻧﻜﻤﺎﺵ ﻋﻤﻮﺩﻱ ﺑﻀﻌﻔَﻴْﻦ ) ﺃﻭ ﺗﻤﺪّﺩ ﻋﻤﻮﺩﻱ ﺑـ 1

2 ﺿﻌﻒ(.



 

( ) ( ) h x g x ,

;

(6) )ﺃ(

x

5 : ( ) ( ) h x g x ,

x

0 : ( ) f x

y

( ) f x



)ﺏ( 0 : ( ) f x , )ﺝ( ﺍُﻧﻈﺮﻭﺍ ﺍﻟﺮّﺳﻢ ﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﺴﺮﻯ . x ;

x

5 : ( ) ( ) h x g x

( ) h x

x

4  ( ) g x

1

– ﺭﻳﺎﺿﻳّﺎﺕ ﻟﻁﻼّﺏ 4 ﻭﺣﺩﺍﺕ ﺗﻌﻠﻳﻣﻳّﺔ – ﺍﻟﺻّﻑ ﺍﻟﺛّﺎﻧﻲ ﻋﺷﺭ – ﺍﻟﻣﻧﻬﺞ ﺍﻟﺟﺩﻳﺩ

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