p q p q p q p q p q p q p q p q p q x y p q t u r s p q p p q p q p q p p p q q p p p q P Q [] p, q P Q [] P Q P Q [ p q] P Q Q P [ q p] p q imply / m

Similar documents

1

[ ] Table

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

名古屋工業大の数学 2000 年 ~2015 年 大学入試数学動画解説サイト

1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2

入試の軌跡

2012 A, N, Z, Q, R, C

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)

4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx

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

x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)

ac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y

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

( ) x y f(x, y) = ax

(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n

ii

Part () () Γ Part ,

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 (

OABC OA OC 4, OB, AOB BOC COA 60 OA a OB b OC c () AB AC () ABC D OD ABC OD OA + p AB + q AC p q () OABC 4 f(x) + x ( ), () y f(x) P l 4 () y f(x) l P

(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


17 ( ) II III A B C(100 ) 1, 2, 6, 7 II A B (100 ) 2, 5, 6 II A B (80 ) 8 10 I II III A B C(80 ) 1 a 1 = 1 2 a n+1 = a n + 2n + 1 (n = 1,

熊本県数学問題正解

A S- hara/lectures/lectures-j.html r A = A 5 : 5 = max{ A, } A A A A B A, B A A A %

行列代数2010A

() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n (

, = = 7 6 = 42, =

ii p ϕ x, t = C ϕ xe i ħ E t +C ϕ xe i ħ E t ψ x,t ψ x,t p79 やは時間変化しないことに注意 振動 粒子はだいたい このあたりにいる 粒子はだいたい このあたりにいる p35 D.3 Aψ Cϕdx = aψ ψ C Aϕ dx

untitled

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

.1 A cos 2π 3 sin 2π 3 sin 2π 3 cos 2π 3 T ra 2 deta T ra 2 deta T ra 2 deta a + d 2 ad bc a 2 + d 2 + ad + bc A 3 a b a 2 + bc ba + d c d ca + d bc +


DVIOUT

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.

.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g(

(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10)

数学Ⅲ立体アプローチ.pdf



(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

( )

( ) sin 1 x, cos 1 x, tan 1 x sin x, cos x, tan x, arcsin x, arccos x, arctan x. π 2 sin 1 x π 2, 0 cos 1 x π, π 2 < tan 1 x < π 2 1 (1) (

newmain.dvi


meiji_resume_1.PDF

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)

x x x 2, A 4 2 Ax.4 A A A A λ λ 4 λ 2 A λe λ λ2 5λ + 6 0,...λ 2, λ 2 3 E 0 E 0 p p Ap λp λ 2 p 4 2 p p 2 p { 4p 2 2p p + 2 p, p 2 λ {

ユニセフ表紙_CS6_三.indd

III No (i) (ii) (iii) (iv) (v) (vi) x 2 3xy + 2 lim. (x,y) (1,0) x 2 + y 2 lim (x,y) (0,0) lim (x,y) (0,0) lim (x,y) (0,0) 5x 2 y x 2 + y 2. xy x2 + y

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0

2. 2 I,II,III) 2 x expx) = lim + x 3) ) expx) e x 3) x. ) {a } a a 2 a 3...) a b b {a } α : lim a = α b) ) [] 2 ) f x) = + x ) 4) x > 0 {f x)} x > 0,

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq

a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p

応力とひずみ.ppt


II (10 4 ) 1. p (x, y) (a, b) ε(x, y; a, b) 0 f (x, y) f (a, b) A, B (6.5) y = b f (x, b) f (a, b) x a = A + ε(x, b; a, b) x a 2 x a 0 A = f x (

Microsoft Word - 触ってみよう、Maximaに2.doc

Ł½’¬24flNfix+3mm-‡½‡¹724

6. Euler x

B ver B

main.dvi

IMO 1 n, 21n n (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a

18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C

2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+

ランダムウォークの境界条件・偏微分方程式の数値計算

simx simxdx, cosxdx, sixdx 6.3 px m m + pxfxdx = pxf x p xf xdx = pxf x p xf x + p xf xdx 7.4 a m.5 fx simxdx 8 fx fx simxdx = πb m 9 a fxdx = πa a =

卓球の試合への興味度に関する確率論的分析

Microsoft Word - 海岸紹介new.doc

16 B

mugensho.dvi

,2,4

レイアウト 1

P1.\..

10_11p01(Ł\”ƒ)

P1.\..

Q34Q35 2

2009 IA I 22, 23, 24, 25, 26, a h f(x) x x a h

II

1.. 1 ll a ii. 1i. i f 1 1 a. a. i. t. 1 fi fi. t i j fj i. j ;i 1. i. aa a

資料5：聖ウルスラ学院英智小・中学校　提出資料（1）

18 ( ) ( ) [ ] [ ) II III A B (120 ) 1, 2, 3, 5, 6 II III A B (120 ) ( ) 1, 2, 3, 7, 8 II III A B (120 ) ( [ ]) 1, 2, 3, 5, 7 II III A B (

untitled

untitled



Taro13-第６章（まとめ）.PDF

2016_Sum_H4_0405.ai


dynamics-solution2.dvi

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2

85 4

(, Goo Ishikawa, Go-o Ishikawa) ( ) 1

120 9 I I 1 I 2 I 1 I 2 ( a) ( b) ( c ) I I 2 I 1 I ( d) ( e) ( f ) 9.1: Ampère (c) (d) (e) S I 1 I 2 B ds = µ 0 ( I 1 I 2 ) I 1 I 2 B ds =0. I 1 I 2

平成 22 年度 ( 第 32 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 ~8 22 月年 58 日開催月 2 日 ) V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2

A

renshumondai-kaito.dvi

ｽﾗｲﾄﾞ ﾀｲﾄﾙなし

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

B. 41 II: 2 ;; 4 B [ ] S 1 S 2 S 1 S O S 1 S P 2 3 P P : 2.13:

Transcription:

P P N p() N : p() N : p() N 3,4,5, L N : N : N p() N : p() N : p() N p() N p() p( ) N : p() k N : p(k) p( k ) k p(k) k k p( k ) k k k 5 k 5 N : p() p() p( )

p q p q p q p q p q p q p q p q p q x y p q t u r s p q p p q p q p q p p p q q p p p q P Q [] p, q P Q [] P Q P Q [ p q] P Q Q P [ q p] p q imply / mpl / (); (). +(tht). ; implictio

( ) A A p q q p A( ) ( A) ( A) (A) A A p ( q r) ( p q) ( p r) ( A ) ( A) ( ) ( A ) A A p q p q ( A ) ( A) ( ) ( ) ( A ) ( ) ( A) ( A ) A A A A p, q P,Q p q p, q, r p q p, q ~ p ot, p p' p p c P p q or p q c p c c p q d p q ( P Q) ( PQ ) q p q p q p q p q q p p if d oly if q iff,,,, [] p q p q p q p q p q p q p q ( p q) q p ( q p) p q ( p q) q p ( q p) p q q p T:true F:fulse T F F T T T T T F T F T T F F F T T T T T F F T F F F F p, q p q ~ ~ ~~ T T T F F T T F F F T F F T T T F T F F T T T T [ p q] [ q p] p q q ~p T T T T T F F F F T T T F F T T p p p p q q p ( p q) r p ( q r) p p p ( q r) ( p q) ( p r) pq p q p p q p q p q p q p q p q p q

P f ( p, q, L, r), Q g( p, q, L, r) ( P Q) ( P Q) P( p, q) Q( p, q) P Q P Q P Q P Q [] IfThe Implies P Q P Q P Q Q P P Q Q P P Q P Q x U P Q P Q p( q( U p( q( p q P P Q Q P P Q Q P x x x x x x x x, p() [Def] p(, q(, r( x x : x x : p( x p( p,q x; p( p(,q( x : p( p( x [Def] X x x R ; x x N; p( ) p( q( x : p( q( x p( q( x U : p( q ( P Q U P Q P Q x P x Q x U : p( q( { x p( } { x q( } x : p( x : p( x : p( x : p( x[ p( q( ] x[ p( q( ] xp( X : p( ) xp( X : p( ) xp( X : p( ) xp( X : p( ) P Q, Q R P R

,,, c : x : x x : x x c x, y R, c xy x or y or A, A O A O O x, y R x y x d,, i y d, ',, ' Q x, x', y, y' Ri ' x x' ' ' x y i x' y' i ' y y' A A A ( A A x A A x x( x ) ( x ) x,, c ( )( )( c ),, c R,, c ( ) ( ) ( c ) p, q p q P Q A, R A A A A A A A x3 x 3 A A A A A A A ( x 3) x 3 A A A A A x 3 x 3 A A A A A A A A x f '( ) x i x x 3 X Y si X siy (, g( A A ( d ) A ( d c ) E O c d f mf ( g( m, x, c d c d x y x y p q

p, q, r, p', q', r' R x px qx r p' x q' x r' x pp' qq' rr' p, q, r, s, p', q', r', s' R rx s, r' x s', x px q p' x q' pp' qq' rr' ss' rx s r' x s' px q p' x q' p q r s rx s r' x s' p' q' r' s' p, q, p', q' Q p q p' q' p p' q q' Ax x A E p, q, r, p', q', r' Q p q r p' q' r' Ax x ( x ) A E p p' q q' r r' Ax x ( A E) x s, t, u, s', t', u' R, s t s' t' s s' t t', s t s' t' s s' t t',, c s t uc s' t' u' c s s' t t' u u' p, q, p', q' R A pa qe p' A q' E p p' q q' A pa qe p' A q' E p p' q q' A ke A E e A A pa qe A p' A q' E p p' q q' Ax x Ay y A( x, ( x, ( x, A E A A E k x x k k x x ( k ) x k x [] s ke te s' t' e s s' t t'

x y x y x y x y x kx 3 x kx 3 x x 3k ( k )( x 3) k x 3 x 3 k 4 x 3 k x k x x 3 k 4 x 3 Y log X Y log X log X log X ( X ) log X log X X Y X Y logy log X X Y X Y X Y logy log X X X Y X X Y X X Y Y X log Y log X X Y X Y X. Y X kx 6 ( x3) log3 ( kx6) log3 ( x 3) log9 ( kx 6) log3 ( x 3) kx 6 ( x 3) x3 kx6 x3 A A 3A E O c d A A ( d) A ( d c) E O c d A 3A E O ( d) A ( d c) E 3A E ( d 3) A ( d c ) E O d c d 3 A E d 3 A A ke A 3A E O p, q, p', q' R k 3k k, A E, E A ke pa qe O A pa qe p' A q' E d 3 d c q p ; A E p p' q q' p d 3 A A ke p q A d c c d p, q d 3 A E, E A d c c d

p q A p q A' ' p q p q p q p q A A p q p q " p q" " q p" x : p( x : p( x : p( x : p( p q p p', q q' p q p q q p P Q x y x y, z N z ( " p q" " q p" q p p q q q q p p q p q q p ( ) P() N ; P( ) ( ) k N ;[ P( k ) P( k )] P( k) P( k) P(k) P( k) ( ) P(), P () N; P( ( ) kn;[ P( k) P( k ) P( k )] ) ( ) P() ( ) k N;[ P() L P( k) P( k )] N; P( ) P( ), P( k) P( k ) P() P( k ) P(k) N; P( ) P() p q P() P( k ) P( k), P( k ) P(k) p(k) k : p( k)

, ( 4 ) N ; ( ) ( ) k kn [ k, ( k ) ( k 4k ) k k k k ( k ) k k { k k ( k ( k ) } ( k ) ] 4k ) x N x ( ) x k ( x kn [( k kx ( k ( k ( k { ( k ) x} k ( ( { ( k ) x} x ( ( k { ( k) x} kx N : x y, N L 3 4 xy x y x y x y x y ( x xy : kn x k k x y y k k N ( ) q( ) p ( ) q () kn ( k ) q ( k ) ( k ), q ( k ) ) x] x k y k x k y k x k y k k k x y xy x y p p p ( k ) q ( k ) p p ( k ) q ( k ) [] k k k 6, 39 ( 4)

( ) R ( ) ( ) ( ) def ( ) ( ) P( ( ) (, ) A Q R P ( ) P( x P( x P( ) A A AE EA E 3 3 3 3 ( )( ) ( )( ) 3 3 3 3 3 3 3 3 ( ) 3 3 ( ) A 3 3 3 c 3c ( c)( c c c) G x ( x )( x x L x ) L x, y I xy x 3y ( x 3)( y ) 6 f ( ) ( ) ( ) f '( c) 5 x 3y 5 y x ( x, ( 3k, k), k I 3 3 x xyy 9 x D y N x, r r ( ) L L ( r,,,, ) r ( x x LL x x p p q c ( k) k ki ( k) ( x ) ( x ) ( A, x ) x )!!) x L x L( ) ( ) ( )( ) ( 3 ( x x x LL x L ( 3! ( ) h ( h) h h LL h h h N x R L ( ) ( )( ) L! 3! 3 e x x x x L! 3! ( c) ( c)( c ) ( c) []! p q r c c ( p q r ) p! q! r! p q r p q

def A A A i A, ( ), c d c d =,=,c=,d=, x x ( x ) 4 4, x x x x x x 4 4 ( )( ) 8 c 3 3 4,, c c [ 5 c 4 5 9 3 c 3 3 3 c 3c ( c)( c c c ), ] i i L i x x ; F( 3 3 3 ( ) cos k, k ) x y,, x, y R; ( x ( )( x y ) k i N; i, i R; ( ii ) ( i )( i ),, L, k,, L,, k i i i f ( g ( dx f ( dx g ( dx t; ( tf g) t; t f t fg f, g ; ( ) t tf g g D 4 fg f g x y x y x y f ( f ( f (x f ( ) ( f ''( ) ), ( ) ( ),, c R; c cc ( ) ( c) ( c ),,,,,, c c c i L L

P() : P( k) P( k ) P(k) P( k ) P( k ) P(k) N; P( ) xy x 3y x, y I Q ( x 3)( y ) 6 ( x 3, y ) (, 6),( 6,),(,6),(6, ),(,3),(3, ),(, 3),( 3,) ( x, (, 4),( 9,3),( 4,8),(3,),( 5,5),(,),(, ),( 6,4) x ( 6) x, 6 8 ( )( ) 7 (, ) (, 7),(,7),(7, ),( 7, ) (, ) (, 8),(,6),(6, ),( 8, ), x 3y 5 x, y I ( x, (, ), 5 y x ( x, ( 3k, k), k I 3 3, ( x y z) x y z x y 3, N z,, 3 x y z z x y z 5 x, y, z d x y z 5 x, y, z X x L X Y Z, X L D x, y, z N x y z x y z x k ( p k q) 57 q ( ) 5 7 N(k) N ( k ) y k p z j ( r j s) M (k) s q M (k) N ( k ) k p x x 9 D 4 p 4 36 j r, ( ) 6 5 4 3 3 4 5 6 4

t [ t ],,,,,,3,5,7,,3,L, p x, y x p, y p N x p y p x y,,, c c c,, c,, 9 3, x y z xy xz yz 5 x y ( x, y, z) p (modp) p p, ( i) S x y x y, 3, 6 p, q, r Q p q r 3 p q r, R f ( x x f ( ), f ( ), f ( 3) x ( x ( 578) 78, (6) 6 [] x, y ( ( ( ( ( x p, q pq ( ) ( k ) k [] () [] [Def] [ ],

2024 © docsplayer.net プライバシー | 利用規約 | フィードバック