さくらの個別指導 ( さくら教育研究所 ) A AB A B A B A AB AB AB B
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2 1 a a a a C a a = = CD CD a a a a a a = a = = D 1.1 CD D= C = DC C D 1.1 (1) () 6 (3)
3 a = C = C C C a a + a + + C = a C 1. a a + (1) () (3) b a a a b CD D = D C C + D = C
4 4 1 1 a + = + a ( a + ) + c = a + ( + c) 1 1 a D c C + a a + a + + c a + + c a a a c a + + c 1. + C + CD = ( + C) + CD = C + CD = D D + C = CD a = a = a + ( a) = + = 0
5 = 0 a + ( a) = 0 a + 0 = a C + C = 0 C a + c = a c a a a b b O + = O O O = O a + ( a ) = a O + = O = O O a (1) () (3) b a a a
6 6 1 1 a 1 a = a + ( ) a a a = 0 D O a + ( ) k a a k k a a 0 1 k > 0 a k a 1 a = a a k < 0 a k a ( 1) a = a 3 k = 0 0 C a = 0 k k 0 = 0 ( ) a = ( a) a 1.3 a c a = 4, 1 c = a a c ( ) (1) = ( ) a () a = ( ) c (3) = ( ) c
7 1.7 a (1) a () (3) a + (4) a a b E k l 1 k(l a) = (kl) a (k + l) a = k a + l a 3 k( a + ) = k a + k 1 3( a) = 6 a = (3 ) a a a a 6 a (3 + ) a = 5 a = 3 a + a 3 a a 5 a 3 ( a + ) = a + a + b a a ( a + ) a
8 (1) 3 a + 4 a a = (3 + 4 ) a = 5 a () ( a + 5 ) + 3( a ) = a a 3 = ( + 6) a + (10 3) = 8 a (1) a + 3 a a () 3 a a (3) 3( a + ) + 4( a ) (4) ( a 3 ) 3(3 a ) (5) 1 3 ( a + ) + 3 ( a ) (6) 1 ( a + ) 1 3 ( a + ) F 0 a a// a a b b a 0 0 a// = k a k 1.5 a = a a a 1 a a e e 4 e a = 3 a a
9 G a a 1.1 CDEF a = a, F = b b F a O C E (1) E () D DF = + (1) E = + E () = a + DF = DC + CF = + ( a) = a a (1) C () EF (3) D P 0 a p a b s t t p b p = s a + t s a O a 1 O P
10 y O x y a e 1 e a = (a O 1, a ) a e (a 1, a ) a a 1 e a = a 1 e 1 + a e 1 O x e 1 a1 e1 a a = (a 1, a ) 1 a 1 a a x y a 1 a e 1 e 0 e 1 = (1, 0) e = (0, 1) 0 = (0, 0) a = (a1, a ) = (b 1, b ) a = a1 = b 1, a = b a = O a = (a1, a ) a = a 1 + a
11 a y a = (3, ) a = 3 + = 13 1 O a d 1 c x 1.11 c d a = (a1, a ) = (b 1, b ) e 1 e a = a1 e 1 + a e = b 1 e 1 + b e y a + = (a1 + b 1 ) e 1 + (a + b ) e a = (a1 b 1 ) e 1 + (a b ) e b a + k k a = (ka 1 ) e 1 + (ka ) e a O b 1 a a 1 x (a 1, a ) + (b 1, b ) = (a 1 + b 1, a + b ) (a 1, a ) (b 1, b ) = (a 1 b 1, a b ) k(a 1, a ) = (ka 1, ka ) k
12 a = (1, 5) = (3, 4) a + 3 = (1, 5) + 3(3, 4) = (, 10) + (9, 1) = ( + 9, 10 1) = (11, ) 1.1 a = (3, 1) = ( 4, ) (1) a () (3) 1 4 (4) 3 a + (5) 4 a 3 (6) ( a ) 1.1 a = (1, ) = (1, 1) c = (5, 4) s t s a + t s a + t = s(1, ) + t(1, 1) = (s + t, s t) c = s a + t y (5, 4) = (s + t, s t) s + t = 5 s t = 4 s = 3 t = c = 3 a + a O c x 1.13 a = (, 1) = ( 1, 3) c = (8, 3) s t s a + t
13 a = (, x) = (1, 3) x a a = k k (, x) = (k, 3k) = k x = 3k x = 3 ( ) = a = (4, x) = (, 1) x C (a 1, a ) (b 1, b ) O = (a 1, a ) y O = (b 1, b ) a = O O = (b 1, b ) (a 1, a ) = (b 1 a 1, b a ) b O a 1 b 1 (a 1, a ) (b 1, b ) = (b 1 a 1, b a ) = (b 1 a 1 ) + (b a ) x 1.8 (, 3) (5, 1) = (5, 1 3) = (3, ) = 3 + ( ) = 13
14 (1) (5, ) (1, 6) () ( 3, 4) (, 0) (1, ) (4, 1) C(5, 3) D(x, y) CD x y D = C y D (x 1, y ) = (5 4, 3 1) C = (1, ) x 1 = 1 y = 1 x = y = 4 O 1 x (1, 1) (4, ) C(5, 4) D(x, y) CD x y
15 O = O + O O O cos θ θ O O cos θ O O O 0 a a = O = O b O θ a θ b a 0 θ 180 O a cos θ a a a = a cos θ θ a a = 0 = 0 a = a = = 3 a θ = 60 a = a cos θ = 3 cos 60 = 3 1 = 3 cos θ θ cos θ a θ a (1) a = 4 = 3 θ = 45 () a = 6 = 6 θ = 150
16 C C = 10 C = 1 cos 10 = C C (1) C () C C O O = a O = O = θ a = O + O O O cos θ θ O a a = a + ( a b) a = (a1, a ) = (b 1, b ) (a 1 b 1 ) + (a b ) = (a 1 + a ) + (b 1 + b ) ( a b) a = a1 b 1 + a b a = (a1, a ) = (b 1, b ) a b = a 1 b 1 + a b a = 0 = 0
17 a = (1, 4) = (, 3) a = 1 ( ) = a a (1) a = (, 5) = (3, ) () a = (1, 3) = ( 3, 3) C a = (a1, a ) = (b 1, b ) 0 θ 0 θ 180 cos θ = a a = a 1 b 1 + a b a1 + a b 1 + b 1.4 a = (1, ) = ( 1, 3) a b = 1 ( 1) + 3 = 5 a = 1 + = 5 = ( 1) + 3 = 10 θ cos θ = a b a = = 1 0 θ 180 θ = 45 ( ) 45
18 (1) a = (, 1) = ( 3, 1) () a = (1, 3) = ( 3, 1) (3) a = (3, 1) = (, 6) (4) a = ( 4, ) = (, 1) 0 a 90 a a a a = a cos 90 = 0 a 0 a a = 0 a a 0 0 a = (a1, a ) = (b 1, b ) a a = 0 a a1 b 1 + a b = 0
19 a = (, 1) = (x, 4) x a = 0 x = 0 a b=x+1 4 x = 1.1 x (1) a = (3, 6) = (x, 4) () a = (4, ) = (x, 1) 1.13 a = (a1, a ) = ( a, a 1 ) a = a1 ( a ) + a a 1 = 0 a c = (a, a 1 ) a 1. a 1 (1) a = (1, 3) () a = (, 5)
20 0 1 D 1 a a = a a = a 3 ( a + ) c = a c + c 4 a ( + c) = a + a c 5 (k a) b = a (k ) = k( a b) k 1 a a 0 a a = a a cos 0 = a a 1 = a cos 0 =1 3 a = (a1, a ) = (b 1, b ) c = (c 1, c ) a + = (a1 + b 1, a + b ) ( a + ) c = (a 1 + b 1 )c 1 + (a + b )c = a 1 c 1 + b 1 c 1 + a c + b c = (a 1 c 1 + a c ) + (b 1 c 1 + b c ) = a c + c ( a b) a b
21 a ( c) = a a c 1.14 ( a + ) ( a ) ( a + ) ( a ) = a ( a ) + ( a ) = a a a b + a b a a= a, a b= a = a ( a + ) ( a ) = a 1.4 a + = ( a + ) ( a + ) a + = a + a b +
22 1 1. a a a = 1, = 4, a b = a = ( a ) ( a ) a a = ( a ) ( a ) = 4 a a a b a + b = 4 a 4 a b + = = 1 a 0 a = 1 = a = 3 = a b = 3 (1) a + () a (3) a
23 x a (1) 3 x 4 a = x () ( x 3 a) = 5( x + ) a = (, 1) (1) a e () a 3 p
24 4 1 3 a = 1 = 3 a = 7 (1) a b () a θ 1 (1) x = a () x = a 10 3 ( (1) 1 e = 5, ) e = ( 1, 5 5 () p = ( 3 5, 6 ) 5 p = ( 3, 5 ) 5 ) 6 5 (1) e = (x, y) a e = 0 e = 1 3 (1) 3 () 150
25 O P p P OP = p O p O P p P P( p) O 1 O = O O b a a ( a) ( b) = a O ( a) ( ) C( c) a c (1) C () C (3)
26 6 1 ( a) ( ) 3 : C c C : = 3 : (3 + ) C = 3 5 c a = 3 5 ( a) ( c = 1 3 ) 3 a + a + 3 b = : 1 D d D D : = 3 : (3 1) 3 D = 3 1 d a = 3 d ( a) b ( d = 1 3 ) 3 a + a + 3 b = m n ( a) ( ) m : n n a + m m + n a 3 a n a + m m n a + n n c C O O
27 ( a) ( ) 4 3 : 4 a = 4 3 a : 1 a + 1 = a ( a) ( ) (1) : 3 () 3 : 1 (3) 4 : 1 (4) 1 : C 3 ( a) ( ) C( c) C G g C D( ( a) d) d = + c 1 C G D : 1 g = a + d d = + c g = a + + c 3 3 ( a) ( ) C( c) C G 1 G( g) ( ) D( d) C( c) g a + + c g = : 1
28 ( a) ( ) C( c) C C C L M N LMN G N ( a) M (1) G g a c ( ) L C( c) () L + M + CN = 0 (1) L M N l m n g = l + m + n 3 l = + c m = c + a n = a + l + m + + c n = + c + a + a + = a + + c () g = l + m + n 3 = a + + c 3 L + M + CN = ( l a) + ( m ) + ( n c) = ( l + m + n) ( a + + c) = 0 LMN G C G OG = OG
29 ( a) ( ) C( c) C C C : 1 P Q R C G PQR G (1) G g a c () G + G + GC = 0
30 d ( a) d d g g P( p) P = t d t 1 P = p a a p = a + t d 1 O p P g 1 t P( p) g 1 g t d g O (x 1, y 1 ) d = (l, m) 1 P(x, y) p = (x, y) a = (x1, y 1 ) 1 (x, y) = (x 1, y 1 ) + t(l, m) = (x 1 + lt, y 1 + mt) { x = x 1 + lt y = y 1 + mt t (x 1, y 1 ) d = (l, m) m(x x 1 ) l(y y 1 ) = d (1) (1, 3) d = (, 4) () (, 1) d = ( 4, 3)
31 ( a) ( ) b 1 a P d = = a p a g p = (1 t) a + t 3 O t = 0 P t = 1 P 0 < t < 1 P t : (1 t) 3 1 t = s p = s a + t s + t = 1 s 0 t ( a) ( ) P( p) p = s a + t s + t =, s 0, t 0 s + t = s + t = 1 s = s t = t s + t = 1 s 0 t 0 p = s ( a) + t () p = s ( a) + t ( ) s + t = 1 s 0 t 0 a O a C P D OC = O OD = O C D P( p) CD
32 ( a) ( ) P( p) p = s a + t, s + t = 1, s 0, t 0 C n ( a) n g P( p) n n P n P = 0 g n ( p a a) = 0 4 p P P p a = 0 4 O 4 ( a) n g n g O (x 1, y 1 ) n = (a, b) 4 P(x, y) p = (x, y), a = (x1, y 1 ), p a = (x x1, y y 1 ) 4 1 (x 1, y 1 ) n = (a, b) a(x x 1 ) + b(y y 1 ) = 0 n = (a, b) ax + by + c = 0
33 n (1) (3, 4) n = (1, ) () ( 1, ) n = (3, 4) C C 3 C C = k k 1.3 CD CD 1 : E D 3 : F 3 F E = D = d F = k E k C = + d = D = d F : FD = 3 : F = + 3 D = + 3 d CE : ED = 1 : D E 1 E = C + D = ( + d) + d = + 3 d F = 3 E 5 3 F E d F 3 C
34 CD C 3 : E D 3 : 5 F 3 F E D C 5 d E F O O C O : 1 D D C P O = a O = b OP a P : PD = s : (1 s) P : PC = t : (1 t) OP a b OP 1 s t P : PD = s : (1 s) OP = (1 s) O + s OD = (1 s) a + 3 s P : PC = t : (1 t) OP = t OC + (1 t) O = 1 t a + (1 t) a 1 t OP a 1 1 s = 1 t, 3 s = 1 t C s O P 1 s D t 1 s = 3 4 t = 1 OP OP = a +
35 O O 3 : C O 1 : D D C P O = a O = OP a 3 O 1 D C a P
36 36 1 = = 3 O O O O O = OC O = C O OC O = C O = C O OC = 0 O = a OC = c OC O = a, OC = c O = a + c, C = a c O = C O = C ( a + c) ( a + c) = ( a c) ( a c) C c O a a + a c + c = a a c + c a c = 0 O OC O OC
37 OC O = OC O C C c O a C C C H H C H C
38 OC O OC : 1 D E O 1 : F 3 D F E C 1 E c 1 F a O D 1 6 O O : 1 C O D D C P s t OP = s O+t O s t (1) OP = s O + t OD () OP = s OC + t O O 1 C P D
39 H = a H = a HC = c H C = 0 HC = 0 H C = 0 H c 5 O = a OC = c DE DF a c DE = DF C 6 s = 1 t = 1 4 (1) () 3 ( ) P D s + t = CD E = D = d d (1) EC D C d E () E (3) E
40 40 1 a = (3, 1) = (1, ) c = a + t t (1) c = 5 t () c c 3 a = = 1 a + a 5 (1) a b () a θ
41 C P Q P Q 3 P = + C Q + Q + CQ = 0 C 5 C O G OH = O + O + OC C (1) 3 O G H H GO C () H C CH
42 4 1 6 C 1 : D C 3 : 1 E C : 3 F E CD P (1) = C = c P c 1 D 3 P F 3 E 1 c C () 3 P F
43 a = 1 = (1) a b () a 8 (a 1, a ) (b 1, b ) O O O = a O = O S S = 1 a ( a b) = 1 a 1b a b 1
44 O O : 1 C C M OM D (1) OD = k OM k O a M C 1 () D : D D 10 C C M + C = (M + M ) M C
45 (1, ) 3x + 4y = 0 H (1) n = (3, 4) H = k n k () H 7 1 cos θ 1 8 S = 1 O O sin O 9 D OD = s O + t O s + t = 1 10 = C = c = 11 (1) H (s, t) 3s + 4t = 0
46 (1) 1 1 b + 1 d () 1 b + 1 d (3) 1 b d (1) t = 3, 1 () c = 5t + 10t + 10 = 5(t + 1) (1) 1 () 60 4 [ + C P = P C 1 : 3 Q + ( Q ) + ( Q C) = 0 4 Q = + C = 3 ] P 5 (1) OH = 3 OG () H C = ( OH O) ( O OC) = ( O + OC) ( O OC) = O OC O = OC H C = 0 6 (1) P = 1 [ 1 b + c (1) P = k E CP : PD = t : (1 t) 6 () P = 5 ] F 6 7 (1) () 3 1 [ 8 O = θ S = 1 a sin θ = 1 a ] 1 cos θ 9 (1) k = 6 5 () : 3 [ (1) O = a O = b OD = 1 k a k ] 10 [ = b C = c M = M = M = M = M = 11 (1) k = 9 5 () ( ) 5, 14 5 ( ) ( ) b + c b + c ( ) ( ) c c ] b
熊本県数学問題正解
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2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l
ABCDEF a = AB, b = a b (1) AC (3) CD (2) AD (4) CE AF B C a A D b F E (1) AC = AB + BC = AB + AO = AB + ( AB + AF) = a + ( a + b) = 2 a + b (2) AD = 2 AO = 2( AB + AF) = 2( a + b) (3) CD = AF = b (4) CE
Part y mx + n mt + n m 1 mt n + n t m 2 t + mn 0 t m 0 n 18 y n n a 7 3 ; x α α 1 7α +t t 3 4α + 3t t x α x α y mx + n
Part2 47 Example 161 93 1 T a a 2 M 1 a 1 T a 2 a Point 1 T L L L T T L L T L L L T T L L T detm a 1 aa 2 a 1 2 + 1 > 0 11 T T x x M λ 12 y y x y λ 2 a + 1λ + a 2 2a + 2 0 13 D D a + 1 2 4a 2 2a + 2 a
(4) P θ P 3 P O O = θ OP = a n P n OP n = a n {a n } a = θ, a n = a n (n ) {a n } θ a n = ( ) n θ P n O = a a + a 3 + ( ) n a n a a + a 3 + ( ) n a n
3 () 3,,C = a, C = a, C = b, C = θ(0 < θ < π) cos θ = a + (a) b (a) = 5a b 4a b = 5a 4a cos θ b = a 5 4 cos θ a ( b > 0) C C l = a + a + a 5 4 cos θ = a(3 + 5 4 cos θ) C a l = 3 + 5 4 cos θ < cos θ < 4
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6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P
6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P
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1 1 f (t) lim t a f (t) = 0 f (t) t a 1.1 (1) lim(t 1) 2 = 0 t 1 (t 1) 2 t 1 (2) lim(t 1) 3 = 0 t 1 (t 1) 3 t 1 2 f (t), g(t) t a lim t a f (t) g(t) g(t) f (t) = o(g(t)) (t a) = 0 f (t) (t 1) 3 1.2 lim
さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n
1 1.1 1.1.1 A 2 P Q 3 R S T R S T P 80 50 60 Q 90 40 70 80 50 60 90 40 70 8 5 6 1 1 2 9 4 7 2 1 2 3 1 2 m n m n m n n n n 1.1 8 5 6 9 4 7 2 6 0 8 2 3 2 2 2 1 2 1 1.1 2 4 7 1 1 3 7 5 2 3 5 0 3 4 1 6 9 1
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8 ) ) [ ] [ ) 8 5 5 II III A B ),,, 5, 6 II III A B ) ),,, 7, 8 II III A B ) [ ]),,, 5, 7 II III A B ) [ ] ) ) 7, 8, 9 II A B 9 ) ) 5, 7, 9 II B 9 ) A, ) B 6, ) l ) P, ) l A C ) ) C l l ) π < θ < π sin
高等学校学習指導要領解説 数学編
5 10 15 20 25 30 35 5 1 1 10 1 1 2 4 16 15 18 18 18 19 19 20 19 19 20 1 20 2 22 25 3 23 4 24 5 26 28 28 30 28 28 1 28 2 30 3 31 35 4 33 5 34 36 36 36 40 36 1 36 2 39 3 41 4 42 45 45 45 46 5 1 46 2 48 3
1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +
( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n
さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1
... 0 60 Q,, = QR PQ = = PR PQ = = QR PR = P 0 0 R 5 6 θ r xy r y y r, x r, y x θ x θ θ (sine) (cosine) (tangent) sin θ, cos θ, tan θ. θ sin θ = = 5 cos θ = = 4 5 tan θ = = 4 θ 5 4 sin θ = y r cos θ =
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
(1) PQ (2) () 2 PR = PR P : P = R : R (2) () = P = P R M = XM : = M : M (1) (2) = N = N X M 161 (1) (2) F F = F F F EF = F E
5 1 1 1.1 2 159 O O PQ RS OR P = PQ P O M MQ O (1) M P (2) P : P R : R () PR P 160 > M : = M : M X (1) N = N M // N X M (2) M 161 (1) E = 8 = 4 = = E = (2) : = 2 : = E = E F 5 F EF F E 5 1 159 (1) PQ (2)
29
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1 I p2/30
I I p1/30 1 I p2/30 1 ( ) I p3/30 1 ( ), y = y() d = f() g(y) ( g(y) = f()d) (1) I p4/30 1 ( ), y = y() d = f() g(y) ( g(y) = f()d) (1) g(y) = f()d I p4/30 1 ( ), y = y() d = f() g(y) ( g(y) = f()d) (1)
HITACHI 液晶プロジェクター CP-AX3505J/CP-AW3005J 取扱説明書 -詳細版- 【技術情報編】
B A C E D 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 H G I F J M N L K Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01
A(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6
1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67
1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 (
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取扱説明書 -詳細版- 液晶プロジェクター CP-AW3019WNJ
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A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)
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1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1
ABCD ABD AC BD E E BD : () AB = AD =, AB AD = () AE = AB + () A F AD AE = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD AB + AD AB + 7 9 AD AB + AD AB + 9 7 4 9 AD () AB sin π = AB = ABD AD
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dynamics-solution2.dvi
1 1. (1) a + b = i +3i + k () a b =5i 5j +3k (3) a b =1 (4) a b = 7i j +1k. a = 14 l =/ 14, m=1/ 14, n=3/ 14 3. 4. 5. df (t) d [a(t)e(t)] =ti +9t j +4k, = d a(t) d[a(t)e(t)] e(t)+ da(t) d f (t) =i +18tj
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1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2
θ i ) AB θ ) A = B = sin θ = sin θ A B sin θ) ) < = θ < = Ax Bx = θ = sin θ ) abc θ sin 5θ = sin θ fsin θ) fx) = ax bx c ) cos 5 i sin 5 ) 5 ) αβ α iβ) 5 α 4 β α β β 5 ) a = b = c = ) fx) = 0 x x = x =
2011de.dvi
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