ΘΕΩΡΙΑ ΜΑΘΗΜΑΤΙΚΩΝ ΚΑΤΕΥΘΥΝΣΗΣ

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    1. 0 ;

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    2. ;

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    1. 1 2 1 2

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    .

    8. ;

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    |z |

    a

    y 5

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    2. f A ;

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    y=f (x) y=| f (x)|

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    11

    a>0

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    :

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    4)1 2 1 2

    log ( ) log log

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    log log x x x x , 0 1 ,

    1 2 1 2log log

    x x x x .

    8) lnx x e , ln e .

    5. f,g ;

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    6. , , f,g ;

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    g f, g

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    .

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    ) , f, g gof fog ,

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    f, g, h ho(gof) , (hog)of

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    ho(gof) (hog)of . f, g h hogof .

    .

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    x A

    ;

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    0x A () , 0f(x ) , 0f(x) f(x ) x A .

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    1 2

    x x , 1 2

    f(x ) f(x ) .

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    .

    11. f A ;

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    1f : 1f(x) y f (y) x

    O x

    y

    y=g(x)

    34

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    ) : 1( ( )) , f f x x x A 1( ( )) , ( ) f f y y y f A .

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    .

    1. f o

    x f o

    x ;

    : f

    0 0(,x ) (x ,) ,

    : 0x x

    lim f(x)

    0 0x x x x

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    ) :

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    3. o

    x .

    :

    ) 1

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    lim f(x) 0

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    x

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    0x x

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    1.0 0 0x x x x x x

    lim (f(x) g(x)) lim f(x) lim g(x)

    2.0 0x x x x

    lim (f(x)) lim f(x)

    , R

    3.0 0 0x