ΜΑΘΗΜΑΤΙΚΑ ΕΠΙΛΟΓΗΣ Γ ΕΠΑΛ

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<ul><li><p> 1 </p><p>: </p><p> . </p><p> : f </p><p> 1 </p><p>,2 1 </p></li><li><p> 2 ... f(x)= 1 . ()=1 </p><p> : 0 0 0 0</p><p>( ) ( ) ( )lim lim lim lim1 1h h h h</p><p>f x h f x x h x hh h h </p><p>+ + = = = = ()=1 </p><p>... (2)=2 </p><p> f()=2 : 2 2 2 2 2</p><p>0 0 0</p><p>0 0</p><p>( ) ( ) ( ) 2lim lim lim( 2 )lim lim ( 2 ) 2</p><p>h h h</p><p>h h</p><p>f x h f x x h x x x h h xh h h</p><p>x h hx h x</p><p>h</p><p>+ + + + = = =</p><p>+= = + =</p><p> (2)=2 </p><p> f R c ,... (cf(x))=cf(x) ,xR </p><p> : 0</p><p>( ) ( )lim ( )h</p><p>f x h f x f xh</p><p>+ = . F(x)=cf(x) : </p><p>0 0 0</p><p>0</p><p>( ) ( ) ( ) ( ) ( ) ( )lim lim lim( ) ( )lim ( )</p><p>h h h</p><p>h</p><p>F x h F x c f x h c f x f x h f xc</p><p>h h hf x h f x</p><p>c c f xh</p><p>+ + + = = =</p><p>+ = =</p><p> ( ( )) ( )cf x cf x = </p><p> f ,g ... (f(x)+g(x))=f(x)+g(x) </p><p> : 0 0</p><p>( ) ( ) ( ) ( )lim ( ) lim ( )h h</p><p>f x h f x g x h g xf x g xh h</p><p>+ + = = </p><p> F(x)=f(x)+g(x) : </p><p>0 0</p><p>0 0 0</p><p>( ) ( ) [ ( ) ( )] [ ( ) ( )]lim lim[ ( ) ( )] [ ( ) ( )] ( ) ( ) ( ) ( )lim lim lim</p><p>( ) ( )</p><p>h h</p><p>h h h</p><p>F x h F x f x h g x h f x g xh h</p><p>f x h f x g x h g x f x h f x g x h g xh h h</p><p>f x g x</p><p>+ + + + += =</p><p>+ + + + + = = + =</p><p> = +</p><p> (f(x)+g(x))=f(x)+g(x) </p></li><li><p> 3 </p><p> : </p><p> : </p><p> , , , , </p><p> : </p><p> : : </p><p> ( ,) v : i , </p><p> i . </p><p> fi i , i . fi = v/ </p><p> 1, 2, ,... ) 0 1if ) f1+f2++f=1 : ) : fi=vi/v 0 iv v </p><p>) : 1 2 1 21 1...</p><p>... ... 1f f f </p><p>+ + ++ + + = + + + = = = </p><p> i </p><p> i </p><p>. i = 1+2++i Fi = f1+f2++fi . </p><p> i i , : 360</p><p>.360o</p><p>o</p><p>i i iv fv</p><p> = = </p><p> . </p><p> , </p><p> . </p><p> (i ,i) (xi, fi) . </p><p> . </p><p>To </p><p> . </p></li><li><p> 4 To </p><p> 1. </p><p> , </p><p> ( ) ( 0). : () , () , () () </p><p> () () () () </p><p> x = x &lt; x &lt; </p><p> : </p><p> ti . 1 1 1</p><p>1 1v k ki i i i i</p><p>i i ix t v x f x</p><p>v v= = == = = </p><p> i ti </p><p> wi </p><p> . . 1 1 2 2</p><p>1 2</p><p>...</p><p>...</p><p>v v</p><p>v</p><p>x w x w x wx</p><p>w w w</p><p>+ + +=</p><p>+ + + </p><p> () , </p><p> . </p><p> : , </p><p> (R) . (s2) ti . </p><p>2 2 2 2</p><p>1 1 1</p><p>1 1( ) ( ) ( )v k k</p><p>i i i ii i i</p><p>s t x x x f x xv v= = =</p><p>= = = i ti </p><p> (s) . 2s s= (CV) : / , 0 / ,s x x s x x &gt; &lt; 0 </p><p> . . </p><p> , . </p><p> : 10%CV </p></li><li><p> 5 </p><p> (..) . </p><p> (..) . (.) .. . </p><p>. </p><p> . .. , </p><p> , .. .. </p><p> , .. </p><p> , </p><p> . ,. B = . A B ( ) . A B ( ) , . </p><p> . - . </p><p> f . / .. . </p><p> { }1 2, ,..., = .. .. . { } { } { }1 2, ,..., </p><p> 1,2,, , </p><p> fi=ki/v : 0 1if f1+f2++f=1 ( ) </p><p> . .. , </p><p> . </p><p> : .. . </p><p> : ( )( ) ( )</p><p>v N AP AN</p><p> = =</p><p> : </p><p> { }1 2, ,..., v = .. . . { }i </p><p> , P(i) , : </p><p>1 20 ( ) 1 ( ) ( ) ... ( ) 1i vP P P P + + + = P(i) . { }i </p></li><li><p> 6 { }1 2, ,..., kA a a a= . () </p><p>1 2( ) ( ) ... ( )kP a P a P a+ + + , . ( ) 0P = </p><p> . , ... ( ) ( ) ( )P A B P A P B = + </p><p> , A B = () = () + () </p><p> : ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( )</p><p>N A B N A N B N A N BP A B P A P BN N N N +</p><p> = = = + = + </p><p>... () = 1- () </p><p> A A = A A = , : </p><p>( ) ( ) ( ) ( ) ( ) ( ) 1 ( ) ( )P A A P A P A P P A P A P A P A = + . = + . = + () = 1-() </p><p> . , .. ... ( ) ( ) ( ) ( )P A B P A P B P A B = + : </p><p> : ( ) ( ) ( ) ( )N A B N A N B N A B = + ()+() A B , : </p><p>( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )N A B N A N B N A B N A N B N A BP A B P A P B P A B</p><p>N N N N N + </p><p> = = = + = + </p><p>( ) ( )A B P A P B . . . : </p><p> : A B ()() ( ) ( )( ) ( )N A N BN N</p><p> . () () . </p><p> . , .. ... ( ) ( ) ( )P A B P A P A B = : </p><p> - A B : </p><p>( ) ( )A A B A B= : ( ) ( ) ( ) ( ) ( ) ( )P A P A B P A B P A B P A P A B= + = </p><p>- A B </p></li></ul>