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1 fx-9750g PLUS CFX-9850GB PLUS CFX-9850GC PLUS CFX-9950GB PLUS J
2 CFX CFX cf u u u u u u
3 u u
4 uu
5 1 o BACK UP 3 BACK UP uu
6 5m 6 defc wc E 7 CFX CFX cf' ed cf' 8m uu
7 CFX u u
8 CFX 3 1 svwf J 6 6 uu
9 uu
10 / fh o!o 1m 2edfc w u u
11 1o 2* +w *( +)w 1!m 2cccc1 3J uu
12 4o 5*sw d e 1d 2dd _ 3f 4w $ { o $$+$ w u u
13 d c!$ d c!$ M M 1o* 2M 3f 4w x y θ r 1m 2d e f c w uu
14 3v(v+ ) (v- )w 46w 1! e 1! g 3 33 uu
15 4d we w 1!Zcc1 2J v(v+ ) (v- )w v+. w 1 36w 1!2 1 2d e f c w u u
16 3d e f c 4w 1m 2d e f c w 3aAvxw 4 44 w 2 uu
17 52w w w 6J 76??=?= uu
18 1m 2d e f c w 3v(v+ ) (v- )w 46w uu
19 u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u uuuuuuuuuuuuuuuuuu u uuuuuuuuuuuuuuuuuu fx-9750g PLUS CFX-9850GB PLUS CFX-9850GC PLUS CFX-9950GB PLUS uuuuuuuuuuuuuuuuuuu u uuuuuuuuuuuuuuuuuu uuuuuuuuuuuuuuuuuuu u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u
20 Σ u u
21 u u
22 u u
23 t u u
24 u u
25 1 6 u 1 1 u g 6 K 6 g CFX u u
26 a u! a u u
27 u u
28 x! a l 10 x 2 B 3 1! a m defc w uu
29 n CFX fx-9750g PLUS uu
30 !Z fc 1 6 J u u u u IH y f(x) y f(x) yif(x) yhf(x) v u u u uu
31 CFX u u u u u u u u u u u u uu
32 u u CFX u u u u Σ Σ u Σ u u u uu
33 CFX u 1 2 x x x x!z fc uu
34 3 Ab/caaw uu
35 ed CFX cf' ed u m!ed! uu
36 !Z 2 3 o m o uu
37 1 uu
38 fc u J π π f c u J 13 n 24 n uu
39 n u u 3 4 µ w A Ac+d-e+baw Ac(f+e)/(cd *f)w uu
40 1 x yr θ Σ d dx d dx dx Σ 2 x x x! 3 x y x 4 a b /c 5 π π 6 e x x A 7 8 n r n r 9 0! GI # e x e x π x e x x y r θ dx d dx A π uu
41 AdEf/hw def/h-ecifhw n uu
42 ( + * w w ** w A d e + - * / π d dxan!6 u!4 1w u A uu
43 d e cga ddd s w e d ed D dgj**c ddd d e![ c.dgx ddddd![ s![ t t![d ew uu
44 r θ a aw AbcdaaAw AaA+efgaaBw w AaAw AaaaAw aa3w r θ Abaa!aA3 Fw uu
45 u K6 g 6 g 3 A (aa+ab) (aa-ab) 11 K6 g 6 g 3 A 21 w K6 g 6 g 3 4 K6 g 6 g 3 A 11 uu
46 x x x y x x x!zc1jk6 g 6 g 3 AvMd+b11x Avx+v12x x A!4 1w!4 5 1 K6 g 6 g w w cf uu
47 uu cf
48 K CFX CFX u u u u u u u u u u u u u u u u u uu
49 J n θθ xyθ u u xy x y u uo p xy uσx Σy xy uσx Σy x y uσxy xy uxσyσ xy uxσyσ x y u x y u x y uu
50 u u u u u u xyxyxy u o xσ u uoo ux σ x σ ux σ u u u u p u ztχ 2 F u uˆˆ ˆ uu
51 u u u u yx!4 5 1 J4 1 cw u u u yx 4w uu
52 u an an an bn bn bn u u aaa u bbb u an bn ann 3w u u uu
53 xy xy 1w x yz xyz xy z 2w x x 3w 4w x x u u uu
54 !W u u u u u^ ^ u u u u u n n u^ u uu
55 2 uu
56 w *-12/-2.5w (2+3)*1E2w 5EE ( + )E ) E * 1+2-3*4/5+6w (2+3)*4w 8E 2+3*(4+5w 29 w (7-2)(8+5)w 65 * 6/(4*5)w E.3 / / w 3 u u uu
57 100/6w !Zccccccccc 15 4 Jw !Zccccccccc 26 g 1 5 Jw E E1!Zccccccccc 3 Jw /7*14w 4EE!Zccccccccc 1(Fix)4(3)Jw 4EE.EEE 200/7w * Ans _ 14w 4EE.EEE 200/7w K6 g 4 4w * Ans 14w aaAw aa/23w 8.4 aa/28w 6.9 uu
58 w Abcd+efgw hij-!kw A w faaaw w Ab/dw *dw x x x!x y x uu
59 e d ue ud Ae.bc*g.ew dddd h.b w A Af c Abcd+efgw cde-fghw A f f d e uu
60 d e Abe/a*c.dw de d![b w u ^ w u ^ ^ w ^ AbcdaaA!W6 g 5 g.j* aa!w5 ^ aa/d.cw ^ w uu
61 u u ux un r n r u u u x u u u u u u u uu
62 u u u u 1 23 n!zcccc1j 4.25K6 g 5 2 w 243.5E7E w E181 uu
63 π n π.!zcccc 1Js63w E.891EE65242!Zcccc 2J c(!7/3)w E.5!Zcccc 3Jt-35w E.6128EE7881!Zcccc 1J 2*s45*c65w E /s30w 2!S0.5w 3E x x uu
64 x e x x y x n l1.23w E.E899E e I90w E967!01.23w e!e4.5w 9E.E (-3)M4w 81-3M4w 81 7!q123w *3!q64-4w 1E x y x n K6 g w K6 g w E.22313E16E1 e I!Kw 1.5 xx e x K6 g 2 5 (20/15)w E xx x K6 g /4w E uu
65 x x x! n!92+!95w 3.65E28154 (-3)xw 9-3xw 9 (3!X-4!X)!Xw 12 8K6 g 3 1 x! w 4E32E!#(36*42* 49)w 42 K6 g 3 4 w E.481E497E11 K6 g 41 l(3/4)w E K6 g w K6 g w K6 g w 3 E.5 4 uu
66 θ θ n xy r θ!zcccc1j K6 g 5 6 g 1 14,20.7)w rθ x y!zcccc1j K6 g 5 6 g 2 25,56)w Ans (r) E19 (θ ) Ans (x) E (y) n r n r n! n! n r n r n r! r! n r! n 10K6 g 3 2 n r 4w 5E4E 10K6 g 3 3 n r 4w 21E uu
67 n 2$5+3$1$4w 3{13{2E M $2578+1$4572w 6.E662E2547E-E4 1$2*.5w E.25 1$(1$3+1$4)w 1{5{7 n!zccccc cccc4j 999K6 g 6 g 1 6 g w 1.E24M 9/10w 9EE.m K6 g 6 g 1 6 g 6 g 3 E.9 3 E.EEE9k 2 E.9 2 9EE.m uu
68 u n 3aaAw 2aaBw aak6(g)6(g) 4(LOGIC)1(And)aBw 1 5aaAw 1aaBw aak6(g)6(g) 4(LOGIC)2(Or)aBw 1 10aaAw K6(g)6(g)4(LOGIC) 3(Not)aAw E u G G G G u G uu
69 3 Σ uu
70 4 u d/dx d /dx dx uσ Σ u f(x) x f(x) n a b uu
71 d dx 2 d dx fx, a, Ax) x d d dx fx a Ax fa dx fa Axf a f a Ax Ax Ax f a f a Axf a f a Ax y fx aa Axaa Ax fa Axfa Ay fafa Ax sy Ax Ax Ax sx Ay Ax sy sx Ay Ax sy sx fa Axfa fafa Ax f a Ax Ax f a Axfa Ax Ax uu
72 y x x xx xax AK4 2 d/dx vmd+ evx+v-g, fx d,x a be-f) xax w fxr θ AxAxAx d d faf a gag a dx dx f ag a f ag a f af a fxa x d xx dx Σ u A u uu
73 d dx 3 d dx fx,a,n) n d fxa n fa dx dx f xhf x hf xf x hf xh f x h x h m d m mhf x m hf x n n n n y x x xx n AK4 3 d dx vmd+evx+v-g, f x d,a g)n w f x r θ n uu
74 d f af a g ag a dx dx f ag a f ag a f af a f xa n d d xx dx Σ u n u A u uu
75 dx 4 dx fx, a, b, tol ) b fx ab tol fx dx a b f x dx a 4 dx fx, a, b, n ) N n n b fx ab n fx dxn n a a x b fx y fxab a x bfx x x dx tol AK4 4 dx cvx+dv+e,fx b,f,a b be-e) tol w f x r θ toln uu
76 toltolnn b a fx dx g x dx b fx dx a b a fx dx fxa b n d c xx dx xx Σ u A u u fx S S b c b fx dx fx dx fx dx a a S c S b fx dx fx dx fx dx fx dx a a x uu x x x b
77 a x b 6 g 1 fx, a, b, n ) n 6 g 2 fx, a, b, n ) n y x xab nx y AK4 6 g 1 vx-ev+j, fx a,d,ab g)n w yx xab nx y AK4 6 g 2 -vx+cv+c, fx a,d,ab g)n w f x r θ n Σ n u ba ba u A u n uu
78 Σ Σ Σ Σ 6 g 3 Σ ak, k, α, β, n ) Σ ak k α β nσak uu ak ak ak Σ ak β S aα aα aβ Σak Σ Σ k kn k AK4 6 g 3 Σ akx-dak+f, ak ak, ak c,g, ak α β b) n w ak ak α β n nn Σ Σ n n Σak n Σbk k k nnnn Σ n n Σak k Σkk Σ Σ Σ n β k α k α u β α β α u Σ AΣ
79 4 uu
80 3 ui i u u u uu
81 i i i AK3 (b+c1 i ) +(c+d1 i )w ii AK3 (c+1 i ) *(c-1 i )w i AK3!9(d+1 i )w a bi Z i rθ AK3 2 (d+e1 i )w AK3 3 (d+e1 i )w uu
82 a bi a bi i AK3 4 (c+e1 i )w a biab i AK3 5 (c+f1 i )w AK3 6 (c+f1 i )w u u u u u x x a b/c d c uu
83 5 uu
84 !Z Jn u u x x x x x x x x u u u uu
85 w A!Z2J11 ccw!z4jw!z5jw n 1 u!z3j A11 bcdw 3 babaw Av Bl CI a b c Ds Ec Ft d e f uu
86 !Z4J Ababbb+bbaba w!z2j A14 bcd* 2 ABCw!Z3Jw uu
87 n 2 u u!z4ja2 1bbaabaw!Z3JAbca2 3ADw!Z5JJAdg2 4J13 bbbaw!z3jja2 2cFFFEDw uu
88 uu
89 6 uu
90 m n mn u u u c cw d w uu
91 c w bwcwdw ewfwgw f c uu
92 cf w u u 1 u u u 1 1 cw dw 1 2 ew cw uu
93 1 3 ew cw dw 1 4 cw dw 2 u u u 2c 1 uu
94 2c 2 2cc 3 3 u u u 3e 1 uu
95 3e 2 3e 3 uu
96 2 u u u u u u n n m m mn nnm mmn m n K2![![b,d,f!]![c,e,g!]!]a1aA w uu
97 K26 g 1 da 6 g 1aA w K26 g 2 6 g 1aA w!{c,d!}ak2 6 g 26 g 1aBw m n m n baak21 aa![b,c!]w K21 aa![c,c!]*fw uu
98 K26 g 3 d,6 g 1aA w K251 aa,1ab w mn m n K221aA, c)ak1 1 bw nα β αβ γ αβγ n uu
99 2 u u u u + - w * 1aA+1aB w 1aA*1aB w uu
100 1aA*6 g 1 c w w e1aa w 3 w 31aAw uu
101 4 w 41aA w!x w 1aA!X w G uu
102 x w 1aAx w M w 1aAMd w w K6 g 41 K21aA w uu
103 u u u u u α α uu
104 uu
105 7 uu
106 u u u uu
107 ax b y c ax b y c ax b y c z d t e u f v g ax b y c z d t e u f v g ax b y c z d t e u f v g ax b y c z d t e u f v g ax b y c z d t e u f v g ax b y c z d t e u f v g 1 u x y z x y z xy z xy z 15 n n 2 ewbw-cw-bw bwgwdwbw -fwewbw-hw 1 abcan bn cnn uu
108 1 1 x y z a a a b b b c c c d d d 1 n w A w n 3 uu
109 ax bx cag ax bx cx dag 2 u x x x 1 2 n n 2 bw-cw-bwcw a b c d 1 1 n uu
110 x x x bw-ewfw-cw 1 x x x bwbwbw-dw 1 w A w de n3 uu
111 3 21 ah!=avat-(b/c)agatxw bew aw cw j.iw f 6 uu
112 f x x x x x u u y sinx a y=e x y=1/x uu
113 u A u A uu
114 uu
115 8 uu
116 cf CFX u u u u u u uu
117 x y!3!3 1 x 2 x 3 x 4 y 5 y 6 y u u xy c 1 θ θ 2 θ θ 3 θ θ r θ θ θ w c uu
118 J!Q w u u u a j. E -f c d e + - * / ( )!7 J!Q - - u u u π u y x u u u u u!31!32 θθθ 2 uu
119 ! θ θ θ uu
120 3 u uih y fxy fxy fxy fx yx 3 1 cvx-f w r θ 3 2 fsdv w x y 3 3 dsvw x dcvw y uu
121 3 4 d w r θ y x x 3 6 g 1 vx-cv-g w yx yx e eeeed w cf 2 1 CFX cf 4 u uu
122 x θ cc 1 cc1 c1 6w!6A u u uu
123 u x y x y u π u uu
124 CFX uu
125 !4 5 dx IH y fxy fxy fxy fx yfx yx x J!4 1w 5 1cvx+dv-e w x x x x x x x x x x x x x x x x x e x x x uu
126 f θ θ θ θ π θπ J!4 1w 5 2csdv w θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ e θ θ θ f g x y θ θ π θ π J uu
127 !4 1w 5 3 hcv-ccd.fv, hsv-csd.fv) w J!4 1w 5 4d w IH y f(x) y f(x) y>f(x) y<f(x) y x x J!4 1w 5 6 g 1vx-cv-g uu
128 w dx y fx xxx dx J!4 1w 5 5 dx (v+c)(v-b) (v-d),-c,b,be-e w!4 1 uu
129 x y u u x x 1 uu
130 d d d e d e d x y f c x f c e e e 1 A uu
131 xye d u u x y u u ^,![,!]w y x x x 3 1 vx+dv-f,![-c,e!]w 6w uu
132 ,![!=,,!]w yx 3 1 aavx-d,![aa!=d,b,-b!]w 6 r θ uu
133 2 u u xy u u y y u u y y x x u u u yxxx 2 1 w 1 uu
134 w 2 6 g 1 u u x y xxx x 2 2 xy 2 fwfw 2 uu
135 J3 4 xy 6 g u u y y y x x y x 2 5y uu
136 y y x x θ 2 6 g d 2 6 g 31 d uu
137 Ax Ay Ax Ay u u u u ^ ^ ^ 6 g 5 uu
138 K1 11 K1 21 uu
139 uu
140 uu
1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C
0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります
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
1 40 (1959 1999 ) (IMO) 41 (2000 ) WEB 1 1959 1 IMO 1 n, 21n + 4 13n + 3 2 (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 = 4, b =
i
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4
35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m
ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4
20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d
i I II I II II IC IIC I II ii 5 8 5 3 7 8 iii I 3........................... 5......................... 7........................... 4........................ 8.3......................... 33.4...................
6. Euler x
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漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト
https://www.hmg-gen.com/tuusin.html https://www.hmg-gen.com/tuusin1.html 1 2 OK 3 4 {a n } (1) a 1 = 1, a n+1 a n = 2 (2) a 1 = 3, a n+1 a n = 2n a n a n+1 a n = ( ) a n+1 a n = ( ) a n+1 a n {a n } 1,
1. 2 P 2 (x, y) 2 x y (0, 0) R 2 = {(x, y) x, y R} x, y R P = (x, y) O = (0, 0) OP ( ) OP x x, y y ( ) x v = y ( ) x 2 1 v = P = (x, y) y ( x y ) 2 (x
. P (, (0, 0 R {(,, R}, R P (, O (0, 0 OP OP, v v P (, ( (, (, { R, R} v (, (, (,, z 3 w z R 3,, z R z n R n.,..., n R n n w, t w ( z z Ke Words:. A P 3 0 B P 0 a. A P b B P 3. A π/90 B a + b c π/ 3. +
X G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2
II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )
II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11
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A 2563 15 4 21 1 3 1.1................................................ 3 1.2............................................. 3 2 3 2.1......................................... 3 2.2............................................
20 4 20 i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1.............................
ii
ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................
1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =
1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i
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18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................
, = = 7 6 = 42, =
http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1 1 2016.9.26, http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1.1 1 214 132 = 28258 2 + 1 + 4 1 + 3 + 2 = 7 6 = 42, 4 + 2 = 6 2 + 8
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)
2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................
Part () () Γ Part ,
Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35
.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(
06 5.. ( y = x x y 5 y 5 = (x y = x + ( y = x + y = x y.. ( Y = C + I = 50 + 0.5Y + 50 r r = 00 0.5Y ( L = M Y r = 00 r = 0.5Y 50 (3 00 0.5Y = 0.5Y 50 Y = 50, r = 5 .3. (x, x = (, u = = 4 (, x x = 4 x,
.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 +
.1 n.1 1 A T ra A A a b c d A 2 a b a b c d c d a 2 + bc ab + bd ac + cd bc + d 2 a 2 + bc ba + d ca + d bc + d 2 A a + d b c T ra A T ra A 2 A 2 A A 2 A 2 A n A A n cos 2π sin 2π n n A k sin 2π cos 2π
73
73 74 ( u w + bw) d = Ɣ t tw dɣ u = N u + N u + N 3 u 3 + N 4 u 4 + [K ] {u = {F 75 u δu L σ (L) σ dx σ + dσ x δu b δu + d(δu) ALW W = L b δu dv + Aσ (L)δu(L) δu = (= ) W = A L b δu dx + Aσ (L)δu(L) Aσ
ORIGINAL TEXT I II A B 1 4 13 21 27 44 54 64 84 98 113 126 138 146 165 175 181 188 198 213 225 234 244 261 268 273 2 281 I II A B 292 3 I II A B c 1 1 (1) x 2 + 4xy + 4y 2 x 2y 2 (2) 8x 2 + 16xy + 6y 2
,. 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,,.
9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,
空き容量一覧表（154kV以上）
1/3 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量 覧 < 留意事項 > (1) 空容量は 安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 熱容量を考慮した空き容量を記載しております その他の要因 ( や系統安定度など ) で連系制約が発 する場合があります (3) 表 は 既に空容量がないため
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)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 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) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
2/8 一次二次当該 42 AX 変圧器 なし 43 AY 変圧器 なし 44 BA 変圧器 なし 45 BB 変圧器 なし 46 BC 変圧器 なし
1/8 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( や系統安定度など ) で連系制約が発生する場合があります (3)
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
熊本県数学問題正解
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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
I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )
I013 00-1 : April 15, 013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida) http://www.math.nagoya-u.ac.jp/~kawahira/courses/13s-tenbou.html pdf * 4 15 4 5 13 e πi = 1 5 0 5 7 3 4 6 3 6 10 6 17
i 6 3 ii 3 7 8 9 3 6 iii 5 8 5 3 7 8 v...................................................... 5.3....................... 7 3........................ 3.................3.......................... 8 3 35
(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
取扱説明書 -詳細版- 液晶プロジェクター CP-AW3019WNJ
B A C D E F K I M L J H G N O Q P 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 00 00 60 01 00 BE EF 03 06 00 19 D3 02 00
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(u(x)v(x)) = u (x)v(x) + u(x)v (x) ( ) u(x) = u (x)v(x) u(x)v (x) v(x) v(x) 2 y = g(t), t = f(x) y = g(f(x)) dy dx dy dx = dy dt dt dx., y, f, g y = f (g(x))g (x). ( (f(g(x)). ). [ ] y = e ax+b (a, b )
W u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)
3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
(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
[ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)
II R n k +1 v 0,, v k k v 1 v 0,, v k v v 0,, v k R n 1 a 0,, a k a 0 v 0 + a k v k v 0 v k k k v 0,, v k σ k σ dimσ = k 1.3. k
II 231017 1 1.1. R n k +1 v 0,, v k k v 1 v 0,, v k v 0 1.2. v 0,, v k R n 1 a 0,, a k a 0 v 0 + a k v k v 0 v k k k v 0,, v k σ kσ dimσ = k 1.3. k σ {v 0,...,v k } {v i0,...,v il } l σ τ < τ τ σ 1.4.
II Time-stamp: <05/09/30 17:14:06 waki> ii
II waki@cc.hirosaki-u.ac.jp 18 1 30 II Time-stamp: ii 1 1 1.1.................................................. 1 1.2................................................... 3 1.3..................................................
2011de.dvi
211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37
(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
![(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y](/thumbs/98/136512264.jpg "(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y")
(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
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
![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](/thumbs/101/149159646.jpg "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")
II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh
1 1.1 ( ). z = a + bi, a, b R 0 a, b 0 a 2 + b 2 0 z = a + bi = ( ) a 2 + b 2 a a 2 + b + b 2 a 2 + b i 2 r = a 2 + b 2 θ cos θ = a a 2 + b 2, sin θ =
1 1.1 ( ). z = + bi,, b R 0, b 0 2 + b 2 0 z = + bi = ( ) 2 + b 2 2 + b + b 2 2 + b i 2 r = 2 + b 2 θ cos θ = 2 + b 2, sin θ = b 2 + b 2 2π z = r(cos θ + i sin θ) 1.2 (, ). 1. < 2. > 3. ±,, 1.3 ( ). A
70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
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,
17 ( ) 17 5 1 4 II III A B C(1 ) 1,, 6, 7 II A B (1 ), 5, 6 II A B (8 ) 8 1 I II III A B C(8 ) 1 a 1 1 a n+1 a n + n + 1 (n 1,,, ) {a n+1 n } (1) a 4 () a n OA OB AOB 6 OAB AB : 1 P OB Q OP AQ R (1) PQ
HITACHI 液晶プロジェクター CP-EX301NJ/CP-EW301NJ 取扱説明書 -詳細版- 【技術情報編】 日本語
A B C D E F G H I 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 K L J Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C RS-232C RS-232C Cable (cross) LAN cable (CAT-5 or greater) LAN LAN LAN LAN RS-232C BE
x V x x V x, x V x = x + = x +(x+x )=(x +x)+x = +x = x x = x x = x =x =(+)x =x +x = x +x x = x ( )x = x =x =(+( ))x =x +( )x = x +( )x ( )x = x x x R
V (I) () (4) (II) () (4) V K vector space V vector K scalor K C K R (I) x, y V x + y V () (x + y)+z = x +(y + z) (2) x + y = y + x (3) V x V x + = x (4) x V x + x = x V x x (II) x V, α K αx V () (α + β)x
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
[ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),
I, II 1, A = A 4 : 6 = max{ A, } A A 10 10%
1 2006.4.17. A 3-312 tel: 092-726-4774, e-mail: hara@math.kyushu-u.ac.jp, http://www.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html Office hours: B A I ɛ-δ ɛ-δ 1. 2. A 1. 1. 2. 3. 4. 5. 2. ɛ-δ 1. ɛ-n
1/1 lim f(x, y) (x,y) (a,b) ( ) ( ) lim limf(x, y) lim lim f(x, y) x a y b y b x a ( ) ( ) xy x lim lim lim lim x y x y x + y y x x + y x x lim x x 1
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A_chapter3.dvi
: a b c d 2: x x y y 3: x y w 3.. 3.2 2. 3.3 3. 3.4 (x, y,, w) = (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, ) xȳw (,,, )xȳw (,,, ) xyw, F F = xy w x w xy w xy w
(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
![(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y](/thumbs/101/151465237.jpg "(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y")
(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
2012 A, N, Z, Q, R, C
2012 A, N, Z, Q, R, C 1 2009 9 2 2011 2 3 2012 9 1 2 2 5 3 11 4 16 5 22 6 25 7 29 8 32 1 1 1.1 3 1 1 1 1 1 1? 3 3 3 3 3 3 3 1 1, 1 1 + 1 1 1+1 2 2 1 2+1 3 2 N 1.2 N (i) 2 a b a 1 b a < b a b b a a b (ii)
0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (,
[ ], IC 0. A, B, C (, 0, 0), (0,, 0), (,, ) () CA CB ACBD D () ACB θ cos θ (3) ABC (4) ABC ( 9) ( s090304) 0. 3, O(0, 0, 0), A(,, 3), B( 3,, ),. () AOB () AOB ( 8) ( s8066) 0.3 O xyz, P x Q, OP = P Q =
7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
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I y = f(x) a I a x I x = a + x 1 f(x) f(a) x a = f(a + x) f(a) x (11.1) x a x 0 f(x) f(a) f(a + x) f(a) lim = lim x a x a x 0 x (11.2) f(x) x
11 11.1 I y = a I a x I x = a + 1 f(a) x a = f(a +) f(a) (11.1) x a 0 f(a) f(a +) f(a) = x a x a 0 (11.) x = a a f (a) d df f(a) (a) I dx dx I I I f (x) d df dx dx (x) [a, b] x a ( 0) x a (a, b) () [a,
29
9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n
y π π O π x 9 s94.5 y dy dx. y = x + 3 y = x logx + 9 s9.6 z z x, z y. z = xy + y 3 z = sinx y 9 s x dx π x cos xdx 9 s93.8 a, fx = e x ax,. a =
[ ] 9 IC. dx = 3x 4y dt dy dt = x y u xt = expλt u yt λ u u t = u u u + u = xt yt 6 3. u = x, y, z = x + y + z u u 9 s9 grad u ux, y, z = c c : grad u = u x i + u y j + u k i, j, k z x, y, z grad u v =
( 12 ( ( ( ( Levi-Civita grad div rot ( ( = 4 : 6 3 1 1.1 f(x n f (n (x, d n f(x (1.1 dxn f (2 (x f (x 1.1 f(x = e x f (n (x = e x d dx (fg = f g + fg (1.2 d dx d 2 dx (fg = f g + 2f g + fg 2... d n n
9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L) du (L) = f (9.3) dx (9.) P
9 (Finite Element Method; FEM) 9. 9. P(0) P(x) u(x) (a) P(L) f P(0) P(x) (b) 9. P(L) 9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L)
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 (
II (1 4 ) 1. p.13 1 (x, y) (a, b) ε(x, y; a, b) 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 x a A = f x (a, b) y x 3 3y 3 (x, y) (, ) f (x, y) = x + y (x, y) = (, )
数学Ⅱ演習（足助・09夏）
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欧州特許庁米国特許商標庁との共通特許分類 CPC (Cooperative Patent Classification) 日本パテントデータサービス ( 株 ) 国際部 2019 年 1 月 17 日 CPC 版のプレ リリースが公開されました 原文及び詳細はCPCホームページの C
欧州特許庁米国特許商標庁との共通特許分類 CPC (Cooperative Patent Classification) 日本パテントデータサービス ( 株 ) 国際部 2019 年 1 月 17 日 CPC 2019.02 版のプレ リリースが公開されました 原文及び詳細はCPCホームページの CPC Revisions(CPCの改訂 ) 内のPre-releaseをご覧ください http://www.cooperativepatentclassification.org/cpcrevisions/prereleases.html
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
1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2
limit&derivative
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欧州特許庁米国特許商標庁との共通特許分類 CPC (Cooperative Patent Classification) 日本パテントデータサービス ( 株 ) 国際部 2019 年 7 月 31 日 CPC 2019.08 版が発効します 原文及び詳細はCPCホームページのCPC Revisions(CPCの改訂 ) をご覧ください https://www.cooperativepatentclassification.org/cpcrevisions/noticeofchanges.html
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