10 1 a 1 aa bb 4 +
b ± b 4ac x a
1 1 CBED DC(BC ED) (a b) DAE CBA DAE 1 ab ABE c 1 1 (ab) c ab
3 4 5 5 1 13 7 4 5 9 40 41 11 60 61 13 84 85 m 1 m + 1 m m ( m 1 ) ( m +1 = ) ()
m AB (m n ) n 1 1 ( m n ) m n AB = m n
x 5y 13z 1000 3x 9y 3z 0 5x 6y 8z 600
9 V D 3 16 ( a b c x x = bc a )
1 6 x + 1 1 x + 1 7 x + 5 + 1 x + 4 = x
s = 8 5 (s ) = 34 (s 3) = 1 5 5
7 355 113
a 1 = a = 1 a n+ = a n a n+1(n 3) a = 1 n 5 [( 1+ 5 ) ( 1+ 5 n ) n ]
a a a 1(n ) n n 1 n+1 a a n = a a m+n m m n 0 [i] i i C = 1 n C = O j n n S n j [ n ] j S = C (n D 1 ) n n j j=0 a = Lim = 5 n 1 = 0.618 n a n+ 1 n n
a n 1 a n a n a n 1
3 5 7 x x x 1706 arctgx = x + + 3 5 7 ( x 1) π 4 = 4arctg(1 5 ) arctg( 1 39 ) π 4 = arctg( 1 ) arctg (1 5 ) arctg( 1 8 )
V c V 0e rc t 1 1 e +! 3! = 4( 1 1 1 1 + + ) 1 3 5 7
α + β = b αβ = c a a
i 1 e f() 1 1 1 1+ + 4 9 16
1 1 4 1 1 + + + L= π 9 16 6 π 6 m = 1 (a b) S = (S S ) 1 S = S + S ( ) 1 1 1 1 p 1+ + LL+ n = p p p 1 p 1 1 p
1
AB AB AB AB AB AOB = AOB = 1 R AB 1 1 1 S RABRBCCD = 1 R (ABBCCD ) 1 SR R = R
MP b = MN a M P M N 1 1 1 1 M P M 3P3 = = = LL= b M N M N a 3 3
M1P1 + MP + M3P3LL = M N + M N + M N LL 1 1 3 3 a b = b a c d a + c c b + d = d 1 4 b = = 1 a 4 πb b = a
0 1 (k) k 0 k 0 k 0 180 180 180
x 1 0 x = 1 x = ± 1 ( ) 1 1 0 5 15 5 15 5 15 5 15 40 1 10
0
W (z + a 1 ) z
log M = log M logn N
dx G x = kx(k dt ) L G T ka dy dt = ka(a TS ) dy dy dt dx = / ka a dx dt = kx = / x dy a 1( ) = 1 dx x log x = y log x = y e 1 e 1 e e
x = 1 1 3 ( 3+ 5) + 3 ( 3 5) 1.10380340 1 3 3 x = 500 + 50000 64 ) + 500 50000 64 ) 8.133360 7 7
3 b y by cy d = 0 y x 3 x (c )x ( b 3 3 b bc d) = 0 3 7 3 p = c q = b 3 b bc d 3 7 3 tu = q () tu = ( p 3 ) 3 (3) () 4(3) (t u) 4tu ( q) 4( p3 3 ) (t u) 3 = q 4( p 3 ) 3 p 3 t u q + 4( ) (4) 3 q q p 3 t = + ( ) + ( ) 3 u = q q p 3 + + ( ) ( ) ( 5) 3
3 3 x = t u (6) x 3 ( t u) 3 3 3 3 3 3 3 t3( t) u + t ( u) u 3 3 3 (t u) 3 t u( t u) p = q 3 x 3 = q px q q x = 3 p 3 + ( ) + ( ) 3 q q + 3 p 3 ( ) + ( ) (7) 3 q q x = 3 + D + 3 D (8) q p 3 D ( ) + ( ) 3 q p 3 P q 0 ( ) = ( ) 0 3 3 3 3 3 3 3 tt ωt ω u u ωu ω q q x 1 = 3 + D + 3 D q x = 3 + 3 q D D x 3 = 3 q + 3 q D D b y x (y ) 3
( 1 bx) (x bx) ( 1 1 b c)x dx f () 4 1 1 (x bx)yy 4 [(x + 1 bx) + 1 y] = ( 1 1 1 b c y)x (byd)xy f 4 4 ( 1 by d) 4(1 4 b c y)(1 4 y f) = 0 (4)
b x a y 0 0 tg 4 = y tg 5 = y 0 0 x c x + c 0 x y = = 1 a b P(x 0 y 0 ) P b x0 tg 3 = a y0 tg 1 tg 180 ( 3 5) tg5- tg3 tg( 5 3) = 1+ tg5tg3 0
y0 + + b x0 x0 c a y0 = 1+ y 0 b x0 ( ) x + c a y 0 b x0 + a y 0 + b cy = 0 (a b )x y + a cy = = 0 0 0 a b + b cx0 b + (a = 0 0 + a cy 0 cy 0 a c x y b cy 0 0 + cx0 ( + cx0) tg tg( 3 4) = tg 3 tg 4 1+ tg( 3tg 4 b x0 y0 + a y0 x0 c = b x 0 y0 1+ ( ) a y x c b cx0 = c x y 0 0 0 a b a cy 0 0 b cx 0 + b x0 a y = ( a b ) x y a cy b ( cx0 a ) = = cy cx a ) 0( 0 0 0 b cy 0 0 0
p y 0 tg 3 = p y y0 tg 4 = y 0 = p x0 p x tg tg tg( 4 3) = 4 tg 3 1+ tg 4 3) y0 p x0 p y 0 y0 px0 + p = = py0 x y py + py 1 + ( x p) y 0 0 px0 px0 + p = x y + py 0 0 0 0 0 0 0 0 p( x0 + p) = = y ( x + p) p y 0 0 0
KPO = π α 3 DOE = π α 3 OPF DOE DOE π α QK 3
3 θ θ cosθ 4cos 3cos 3 3 cos10 = 1 cos40 = x
GA AC FD GA ED
d AC AB ED
1 S 1 1 n 1 1 = ( + ) m + n m m 1 1n 1n = + 3 LL m m m 1 1 1 1 = + m m m m
1 m 1 1 1 1 1 1 x = 1 x x x 3 1 = 1 1 1 1 1 1 1 1+ x = 1 x x x 3 1 = 1 1 1 1 1 1 0 1 893 0 893 0 = 893 1 0 1 1 0 1
1 10 1 10 1 1 100 1000 1 100
1 1 1 + + + 10 100 1000 1 10 1 = = 1 9 1 10 1 1 1 1+ + + + 10 100 1000 1 10 = = 1 9 1 10 10 1 ( ) = 1 9 9 1 9 1 1 1 1 1 1 1 1 4 8 16 3 t )
xy = 100 (1) x(5 x) = y(5 y) () x y 0 x y 5
AC AD AC AD BC BD = BC BD
AB + BD BD BE BC AB + BD BD BE = BD AB BC BE = AB BD BE BC BD AB AB BD = BC BD BC AB BCBD AB BCBD = BC BD
64 64 4 3 16 3 1 3 1 64 64 3 4 1 4 64 64 ( 3 4 1 4
n = 1N an N n 1 3 A B AB a ( ) 1 3 1 3 1
1 4 1 1 M AB 4 AB 1 4
3 4 )
1 4 34 n n(n 1)
46 81 117 10 15 76 00 03 19 60 3 175 54 69 153 78 16 161 17 5 171 90 58 75 135 114 50 87 184 189 13 68 150 61 45 38 91 136 9 7 119 104 108 3 174 5 57 30 116 5 133 10 51 6 16 07 39 34 138 43 100 9 105 15 47
D D 3 D 4 D5 5 D 6 = 1 = = D D D 3 4 D n+ 1 4n 6 = D n n 5
1 () 360 k 3 4 6 k a ( ) p () a 0.387 0.73 1 1.54 5.03 9.539 p 0.41 0.615 1 1.881 11.86 9.46
a ( )p () lga 0.41 0.141 0 0.183 0.716 0.980 lgp 0.618 0.11 0 0.74 1.074 1.469 ω = f ( z ) 1 a = ( z + z ) 1 a ω = ( z + ) z
v 1 = ic tgψ1 v ic tgψ tgψ 1 + ψ v = ictg( ψ 1 + ψ ) = ic 1 tgψ1ψ v + v 1 = v1 v 1 + ( )( ) c c n n M ini f = = [ y ( Ax + B)] i= 1 i= 1 i i
N S N S 1 3 B 1 B B 3 A 1 3 1 A 1 0 3
p* 3 3 1 A1 4 4 4 3 A E
1 a f( x) = ( x + ) ( a 0) x x* = a x0 0 1 a xn+ 1 = f ( xn ) = ( x n + ) xn {x n } a a