2011~ 2012
2012 7
120
A
_
(2' 7 14' )
1. ABC ABC D
A. A B C
C AB AC BC
2 AB P(A)=
A
B ABC
D ABC ABC ABC
1
P(B)>0 P(A|B)=(D)
3
1
15
B
1
5
4
1
D
15
3
3 X [-12] X f (x)(A)
C
1
, 1 x 2 ;
A f ( x) 3
0,
.
1, 1 x 2 ;
.
C f (x) 0,
3, 1 x
c 0
sin x cos x
x x 1
cos x sin x
tan x sec 2 x
sec x sec x tan x
ex ex
log a
x
csc x csc x cot x
ln x
a x a x ln a
x ln1 a
arctan x
cot x csc 2 x
arcsin x
1
1
x
1
arccos x
1 x2
1
1
arc cot x
2
1 x
1 x2
x 1
x
1 x2
21x
u v u
1 0, 1 , 2 ,K , n x1 , x2 ,L , xn .
1
2 c
1
,0 x ,0
.: (1) f ( x; )
,
0,
L( ; x1 , x2 ,L , xn )
1
, 0 xi , i 1, 2, L n x( n ) , ( n ) .
n
y
1
n
,
(2) ( n ) g n ( y ) n( ) n 1 , 0 y , E ($L ) 0 yg n ( y )dy
n 1
c
n 1
.
n
2. N ( , 2 ) , 16 x 240