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