1、 2015/12/21 1 2015/12/21 2015/12/21 10 15 16 + - 2015/12/21 1631 1998 1659 1557 17 1693 19 20 2015/12/21 1859 x,y,z , , 1919 2015/12/21 - 2015/12/21 2015/12/21 , 2015/12/21 2015/12/21 x 7+( )=16? 2015/12/21 1. a+b =b+a a b 2. x, y 3. 4. 2015/12/21 2015/12/21 3 (12-7), ax-by+3z, n!, xdx+ydy, sinxdx x
2、,y,z 2015/12/21 sin, cos, lg, a x (x ) , k n 2015/12/21 15 F x ,y ,z F 1 1 1 2 2 2 12 ( 1) s s s k l q k l q k l q s Ax y z A x y z Ax y z s 1 . i i i k l q i i i i Ax y z A k l q + +.+ 1,2,., i i i k l q i s () 2015/12/21 16 22 2 2 2 2 2 2 , , , , , ax bxy cy dx ey f ac b af d cf e a c f 2015/12/21
3、 17 ( , , , ) ( , , , ) P x y z Q x y z ( , , , ) ( , , , ) 0 P x y z Q x y z 1 1 1 1 a a b a c a d b b a b c b d c c a c b c d d d a d b d c 2015/12/21 18 n A A n ( 0, , 1), n a A A n N n n A 2 4 ab ab ba a b ab 2015/12/21 19 ( ) 1 N ,N a a 1N N log . a a aN 2015/12/21 20 0 1. 0, 1 aa 1 2. , 0, , 1
4、 q q a a a q N q 3. , 0, , , 1 p q p q a a a p q N q 1 4. , 0, s s a a s a 5. lim lim nn nn a a a a 1 , 10 nn n - 1 6. aa a 2015/12/21 21 C(x) S(x) 2 4 6 3 5 7 ( ) 1 , 2! 4! 6! () 1! 3! 5! 7! x x x Cx x x x x Sx 2015/12/21 22 arcsin ,arccos xx -1 1), sin(arcsin ) ,cos(arccos ) , - arcsin 0 arcsin 22
5、 x x x x x xx ( 2015/12/21 2015/12/21 x-x=0; 0 x=0; sin 2 x+cos 2 x=1, ? : 2015/12/21 x-x=0; 0 x=0; sin 2 x+cos 2 x=1, x 2 +y 2 =1 2015/12/21 2015/12/21 2015/12/21 1. 2015/12/21 a b b/a m 1 a,b,m b a. b/a (a+m)/(b+m) a/b c/d a/b (a+c)/(b+d) c/d. 22 , ab 22 cd 2015/12/21 (a 2 +b 2 )(c 2 +d 2 )(ac+bd)
6、 2 =(a,b), =(c,d), , . =ac+bd. 2015/12/21 , B = B 1 =B 2 = = B n =A 2. 2015/12/21 b(a+m) a(b+m) ab bm am b/a (a+m)/(b+m) m 0 b a B = B1 = B2 = = Bn = A 2015/12/21 3 a 0,b 0,2c a+b 22 . c c ab a c c ab pp 22 . c c ab a c c ab pp 22 . c ab a c c ab pp 2 . a c c ab p 2 2 . a c c ab p a 0 a-2c -b a+b 2c
7、, 2 2. a ac ab p2015/12/21 3. C A B 4. C A C B P46 4. 2015/12/21 5 a.b R f(x) R + . 1 1 1 a b b a a b a b ( ) 0 . 1 x f x x x , a b a b ( ) ( ). f a b f a b 11 a b a b a b a b . 11 ba a b a b . 11 ba ab 2015/12/21 5. 6. , , , P48 8. 2015/12/21 2015/12/21 1. 2015/12/21 1 p R IpI 2 (log 2 x) 2 +plog 2
8、 x+1 2log 2 x+p log 2 x p x 2015/12/21 log 2 x=a, (a-1)p+a 2 -2a+1 0, 2(a-1)+a 2 -2a+1 0, -2(a-1)+a 2 -2a+1 0. a 3 a -1 x 8 0 x 1/2. f(p)=(a-1)p+a2-2a+1, f(p) 0 f(2) 0 f(-2) 0 2015/12/21 2. P52 2. 2015/12/21 3. 4 x x+a y = y=x+a, 22 2 ax 22 2 ax y= y= y= 22 2 ax y= y=x+a, x 1 =0 x 2 = - 2a/3 2015/12/21 a0 y 0 x xI - 2a/3 x 0. 2015/12/21 4. P55 5( 4 ).
