A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3

Similar documents

熊本県数学問題正解

取扱説明書　-詳細版-　液晶プロジェクター　CP-AW3019WNJ

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】

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

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

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

f (x) x y f(x+dx) f(x) Df 関数接線 x Dx x 1 x x y f f x (1) x x 0 f (x + x) f (x) f (2) f (x + x) f (x) + f = f (x) + f x (3) x f

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

BD = a, EA = b, BH = a, BF = b 3 EF B, EOA, BOD EF B EOA BF : AO = BE : AE, b : = BE : b, AF = BF = b BE = bb. () EF = b AF = b b. (2) EF B BOD EF : B

高等学校学習指導要領

高等学校学習指導要領

1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 :

高校生の就職への数学II

1 26 ( ) ( ) 1 4 I II III A B C (120 ) ( ) 1, 5 7 I II III A B C (120 ) 1 (1) 0 x π 0 y π 3 sin x sin y = 3, 3 cos x + cos y = 1 (2) a b c a +

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

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 ) = (,

a (a + ), a + a > (a + ), a + 4 a < a 4 a,,, y y = + a y = + a, y = a y = ( + a) ( x) + ( a) x, x y,y a y y y ( + a : a ) ( a : a > ) y = (a + ) y = a

入試の軌跡

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

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

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

日立液晶プロジェクター CP-AW2519NJ 取扱説明書- 詳細版-

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

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. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 = 4. () = 8 () = 4

数学Ⅲ立体アプローチ.pdf

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

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

空き容量一覧表（154kV以上）

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

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

05‚å™J“LŁñﬁ~P01-06_12/27

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,

‚å™J‚å−w“LŁñﬁ~P01†`08

122 6 A 0 (p 0 q 0 ). ( p 0 = p cos ; q sin + p 0 (6.1) q 0 = p sin + q cos + q 0,, 2 Ox, O 1 x 1., q ;q ( p 0 = p cos + q sin + p 0 (6.2) q 0 = p sin

高等学校学習指導要領解説　数学編

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 (

案内（最終2）.indd

0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ). f ( ). x i : M R.,,

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

案内最終.indd

05秋案内.indd

( ) a, b c a 2 + b 2 = c : 2 2 = p q, p, q 2q 2 = p 2. p 2 p q 2 p, q (QED)

, x R, f (x),, df dx : R R,, f : R R, f(x) ( ).,, f (a) d f dx (a), f (a) d3 f dx 3 (a),, f (n) (a) dn f dx n (a), f d f dx, f d3 f dx 3,, f (n) dn f

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

０４年度LS民法Ⅰ教材改訂版.PDF

A B C D E F G H J K L M 1A : 45 1A : 00 1A : 15 1A : 30 1A : 45 1A : 00 1B1030 1B1045 1C1030

SIRIUS_CS3*.indd

A A. ω ν = ω/π E = hω. E

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)

Solutions to Quiz 1 (April 20, 2007) 1. P, Q, R (P Q) R Q (P R) P Q R (P Q) R Q (P R) X T T T T T T T T T T F T F F F T T F T F T T T T T F F F T T F

(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

春期講座 ~ 極限 1 1, 1 2, 1 3, 1 4,, 1 n, n n {a n } n a n α {a n } α {a n } α lim n an = α n a n α α {a n } {a n } {a n } 1. a n = 2 n {a n } 2, 4, 8, 16,

76 3 B m n AB P m n AP : PB = m : n A P B P AB m : n m < n n AB Q Q m A B AQ : QB = m : n (m n) m > n m n Q AB m : n A B Q P AB Q AB 3. 3 A(1) B(3) C(

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

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

1 180m g 10m/s v 0 (t=0) z max t max t z = z max 1 2 g(t t max) 2 (6) r = (x, y, z) e x, e y, e z r = xe x + ye y + ze z. (7) v =

Z: Q: R: C: 3. Green Cauchy

Z...QXD (Page 1)

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

() 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)

PROSTAGE［プロステージ］

取扱説明書［F-12C］

4STEP 数学 B( 新課程 ) を解いてみた平面上のベクトル 6 ベクトルと図形 59 A 2 B 2 = AB 2 - AA æ 1 2 ö = AB1 + AC1 - ç AA1 + AB1 3 3 è 3 3 ø 1

r 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B

Transcription:

π 9 3 7 4. π 3................................................. 3.3........................ 3.4 π.................... 4.5..................... 4 7...................... 7..................... 9 3 3. p N p N............................ 3.................................. 3.3............................ 3 4 4 4.................................. 4 4........................ 4 4.3........................ 7 5 5...............................

A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3

. r πr πr n n n n r πr r πr = πr : (4.3 B a O C A 3: N p N N s N s N p N 3

N a p N = (N a/ = Na 3 OA =, BC = a OAB s N = (N a = a ( a = Na = p N ( N s N N p N N s N = p N π π.4 π a r = na S S = πr = πn a M B Ma < S = πn a < (M + Ba, M n < π < M + B n a =, r = n ( n π (. n = 4 π (M, B /4 4.5 ( ( x- y- k /4 N x- P k = N,, k =,,..., N P k y- Q k Q k = k ( k N, N 4

4: π 5

Q k R k Q k O P k P k 5: (N = A Q k Q k+ O P k P k+ 6: (N = A 6

Q k x- P k Q k R k /4 π/4 P k P k Q k R k k =,,..., N ( 5 /4 π/4 P k P k+ Q k+ Q k k =,,..., N ( 6 N k= ( k < π N N 4 N N k= N 4 < k= N k < π < 4 N ( k. N N N k= N k. ( N π ( 4/N N = 3.4 < π < 3.43. N = ( π. N N a N b N a N b 7 OBA = EBD OAB EDB OA =, ED = AE = b, AB = b OA : ED = AB : DB, : b = b : DB, DB = bb. (3 ODC = EBD OCD EDB OD =, EB = AB AE = b b, CD = a OD : EB = CD : BD, : (b b = a : BD, BD = a(b b. (4 (3 (4 bb = a(b b, b (a + b = ab, b = ab a + b. (5 OAF = DAC OF A DCA OA =, DA = F A = a, AF = a OA : DA = AF : AC, : a = a : AC, AC = a. (6 7

D B a F E b a b O C A 7: EOA = AOF OAE OF A OAE DCA OA =, DC = a, AE = b OA : DC = AE : CA, : a = b : CA, CA = ab. (7 (6 (7 a = ab, ab a =. (8 N p N N q N p N = Na, q N = Nb, p N = Na, q N = Nb a = p N /N, b = q N /N, a = p N /(N, b = q N /(N (5, (8. q N = p Nq N p N + q N p N = p N q N (p N q N, (p N q N. 8

6, 4, 48 96 9 p 6 = 3, q 6 = 3 q = 3 3 3 + 3 = ( 3, p = 3 ( 3 = 6 3. p N < π < q N n =, 3.58 < π < 3.53, n = 4, 3.36 < π < 3.596, n = 48, 3.393 < π < 3.46, n = 96, 3.4 < π < 3.47, n = 9, 3.44 < π < 3.48. π 96 3.4 9 3.4 3. p N, q N N =, 4, 48, 96, 9. a, b A(a, b = a + b, G(a, b= ab, H(a, b = ab a + b A(a, b a b, G(a, b, H(a, b A(a, b G(a, b a = b 4(A(a, b G(a, b = (a + b 4ab = a + ab + b 4ab ( A a, = b = a ab + b = (a b. ( a + = a + b b ab = H(a, b 9

( H(a, b = A a, ( G b a, = b ab, H(a, b ab = G(a, b H(a, b G(a, b A(a, b max(a, b = { a, a b, b, a < b, min(a, b = { a, a b, b, a > b, a max(a, b, b max(a, b A(a, b = (a + b (max(a, b + max(a, b = max(a, b a min(a, b, b min(a, b ( A a, = ( b a + ( b min(a, b + = min(a, b min(a, b, H(a, b = A (, min(a, b. a b min(a, b H(a, b G(a, b A(a, b max(a, b p N < q N q N = H(p N, q N, p N = G(p N, q N p N < p N < q N < q N p 3 n q 6 α q 3 n p 6 β n q 3 n+ = H(p 3 n, q 3 n β = H(α, β = αβ α + β α + αβ = αβ, α = αβ, α = β α π

3 3. p N p N N 6 p N p N 7 DCA DC = a, CA = a, DA = a a + (a = (a a = p N /N, a = p N /(N p N N + p4 N 4N = p N 4 N, p4 N 4N p N + 4N p N =, p N = N ± = N ( N ± p N = N 4N 4 4N p N = N ± N N p N. N p N p N < q N < q 6 = 3 ( N, p N = N N p N ( N N p N. (9 3. (64? 78 a n = p 3 n {a n } a n+ a n a n+ a n+ a n+ a n.5 = 4 t N = N N p N N p N = Nt N, N ( t N = p N, N t N = N p N N N (9 p N = N ( N (N t N = (N p N N p N = N ( t N, (N t N = (N p N = 4N N ( t N = N ( + t N.

n 3 n a n+ a n+ a n a n+ a n a n+ a n 6 3..588543.5344939 3.588543.6875.58493988 3 4 3.368638.67589766.59585 4 48 3.3935347.68747844.5565 5 96 3.439589.45395.5557 6 9 3.4454785.53566.5337488 7 384 3.4557679.68436.5784376 8 768 3.45838948.6578 : t N = ( + t N, p Nt N = N ( t N ( + t N = N ( t N = p N. p N t N = p N, t N = ( + t N ( ( N = 3 n a n = p N, a n+ = p N ( t N = p N (N a n+ a n = p N p N = p N p N t N = p N ( t N = p N( t N + t N p 3 N = (N ( + t N. a n+ a n+ = p 4N t 4N = p N a n+ a n+ = p 3 4N (4N ( + t 4N. p 3 N (4N t 3 4N ( + t 4N.

a n+ a n+ a n+ a n = p3 N (N ( + t N p 3 N (4N t 3 4N ( + t 4N = + t N 4t 3 4N ( + t 4N n N = 3 n p N π t N = N N p N = p N N t N, t 4N ( a n+ a n+ a n+ a n = + t N 4t 3 4N ( + t 4N + 4( + = 4 (. n a n+ a n+ a n+ a n 4 3.3 a n π b n b n = 4a n+ a n ( 3 n b n 4π π 3 = π b n+ b n = 4a n+ a n+ 4a n+ a n 3 3 = 4(a n+ a n+ a n+ a n 3 = 4(a n+ a n 3 ( 3 an+ a n+ a n+ a n 4 n b n a n π π 6 4. a n ( b, b, b 3, b 4, b 5 3

4 7 674 4 ([] ( ([] 4. < r < S n = + r + r + + r n + r n rs n = r + r + r 3 + + r n + r n+ S n rs n = r n+, ( rs n = r n+, S n = rn+ r n r n+ + r + r + + r n + r n + = lim n S n = r (3 r = + + 4 + 8 + = 8 4. 9 OA =, AC = a OAB S(a < a S(a a < r < n AC C n AC n = ar n C = C OC n B n B n OC n D n OC n C n C n C n = r n a r n a = a( rr n a( rrn OB n D n OC n C n OB n =, OC n = + a r n 4

8 6 4 8: + + 4 + 8 + 6 + = C B D D B D 3 B B 3 C C C 3 a O 9: A 5

OB n D n OC n C n : ( + a r n OB n D n a( rr n ( + a r n = a( rrn n =,,... n= a( rr n ( + a r n ( a r n + a 4 r 4n a 6 r 6n + a( r a( rr a( rr a( rr3 = + + + ( + a r ( + a r 4 ( + a r 6 ( + a r 8 + a( r ( = a r + a 4 r 4 a 6 r 6 + a( rr ( + a r 4 + a 4 r 8 a 6 r + a( rr ( + a r 6 + a 4 r a 6 r 8 + a( rr3 ( + a r 8 + a 4 r 6 a 6 r 4 + + a( r ( = a r + a 4 r 4 a 6 r 6 + a( r ( + r a r 5 + a 4 r 9 a 6 r 3 + a( r ( + r a r 8 + a 4 r 4 a 6 r + a( r ( + r 3 a r + a 4 r 9 a 6 r 7 + +. 6

a( rr n a( r = ( + r + r + r 3 + ( + a r n n= a( r (a r + a r 5 + a r 8 + a( r + (a 4 r 4 + a 4 r 9 + a 4 r 4 + a 4 r 9 + a( r (a 6 r 6 + a 6 r 3 + a 6 r + a 6 r 7 + a( r = ( + r + r + r 3 a( r + a r ( + r 3 + r 6 + a( r + a 4 r 4 ( + r 5 + r + r 5 + a( r a 6 r 6 ( + r 7 + r 4 + r + ( a( r = r a r r + a4 r 4 3 r a6 r 6 5 r + 7 = (a a3 r + r + r + a 5 r 4 + r + r + r 3 + r a 7 r 6 4 + r + + r +. 6 r OB n D n OAB S(a r a n+ r n an+ + r + + rn n + S(a = (a a3 3 + a5 5 a7 7 +. (4 a = OAB π /8 8 π = S( = ( 3 + 5 7 +, 3 (. π = 4 ( 3 + 5 7 +. 4.3 π π (4 π 7

C G b + a F E B a O D : A OA =, AB = a, BC = b OB, OAB = 9, OBC = 9, < a, b < C OA CD CD OB E B CD BF c = DC/OD OAG S(c = S(a + S(b c a, b OAB ODE, ODE BF E, BF E CF B OAB CF B OB : CB = AB : F B, OA : CF = AB : F B CB = b OB, AB = a OB : b OB = a : F B, F B = ab OA = : CF = a : ab, CF = b CD = DF + F C = AB + F C = a + b, OD = OA DA = OA F B = ab, c = CD OD = a + b ab. 8

S ( a + b = S(a + S(b (5 ab (5 a =, b = 3 + 3 3 = π 8 = S( = S ( + S ( 3 : S(/ + S(/3 = S( 4 (. ( π = 6 5 3 5 + 3 5 5 5 7 5 + 7 9 5 9 5 + ( 4 39 3 39 + 3 5 39 5 7 39 + 7 9 39 9 39 +. (6 9

[ ] (5 S ( = S 5 ( + S 5 ( = S 5 5 + 5 5 5 = S ( 5. (5 4S ( ( ( 5 5 = S + S = S 5 5 + 5 5 5 = S (. 9 S( + S ( = S 39 S( + S + 39 39 = S ( ( = 4S, 39 5 ( ( S( = 4S S. 5 39 (. 9 S( = π 4 (4 5. (6 5 6 π 5 5. a > b a = a, b = b, a n+ = a n + b n, b n+ = a n b n n =,,,... {a n }, {b n } b < b < b < < b n < b n+ < a n+ < a n < < a < a < a.

b n b n+ a n+ a n lim n a n = α, lim n b n = β α = lim n a n+ = lim n a n + b n = α + β α = β α a b M(a, b. M(, n a n b n a n b n....5.4435637.8578643763.4576789.45647535.634666 3.45679485.45679394.34 4.4567935.4567935. (a n+ b n+ = (a n + b n a n b n = ( an b n (a n b n = ( an +. (7 b n a n > b n < a n b n < N < a n+ b n+ < N (. a =, b = c =, a n+ = a n + b n, b n+ = a n b n, c n+ = a n b n, n =,,... π = M (, n c n n=. s n = n k= k c k, p n = a n s n

p 3. 8767 647 8 67 999 755 3693 65 p 3. 468 93 97653 939 874 456 938 7957 p 3 3. 459 6538 95446 496 947 5888 4348 688 p 4 3. 459 6535 89793 3846 6366 76 633 7577 p 5 3. 459 6535 89793 3846 6433 8379 588 497 π 3. 459 6535 89793 3846 6433 8379 588 497 p 3 9 p 4 p 5 4 π π p π 799 6. ( p, p, p 3 A a a k a = k a a k k a b = k a > b b = b n + b n + + b n + b n + b n+ + b n+ 4 + b i 99 b ( n b < n+ n b < n+ i =,,... Y i = b i + b i + + b i + b i X i X i Y i X i = c i + c i + + c i + c i, c, c,..., c i 9 X i = Z + c i, Z = c i + c i + + c i

Z (X i + c i = X i Y i = Y i + b i < (Y i + Z < Y i +, Z Y i (Z+ > Z+c i = X i X i (Z + > Y i = Y i + b i Y i. (Z + > Y i Z Z Y i Z = X i c i Z + Zc i + c i = X i Y i = Y i + b i, Zc i + c i (Y i Z + b i (8 (Y i Z + b i Z Q ZQ (Y i Z + b i < Z(Q + Z(Q + + (Q + > Z(Q + > (Y i Z + b i c i Q c i c i = Q c i = Q c i = Q X n Y n b < (X n + X n X n b = k a < X n + k X n a < k X n + k a k. 3 4 3

7 7 3 4 3 3 3 4 6 3 4 6 4 3 4 6 4. 7 3 3 89 9 7 69 4 76 76 c 3 7 ( + c c (c = 9 c = 8 3 ( 7 + c c ( 89 = ( 34 3, c = 3 3 ( 73 + c 3 c 3 ( 9 = 7 (7 346, c 3 = 3 =.73 7. 3 3 3 =.73 3 =.679 5 5 7 7 3 4. 5 7. 6 79 6 5 79 78 7 49 6 5.679 =.57.68 =.57 3 =.57 q = ( 3 <.68 = 3.6 4

7 p = 6 3 3. = 6.57 < p < 6.58 = 3.8 p < π < q 3. < π < 3.6 B ([3] k <. K(k = E(k = dx ( x ( k x = dθ k sin θ (, k x π dx = k x sin θ dθ (. x = sin θ. a > b >, k = b a I(a, b = J(a, b = cos θ = sin θ I(a, b = J(a, b = dθ a (a b sin θ = a a (a b sin θ dθ = a dθ a cos θ + b sin θ, a cos θ + b sin θ dθ dθ k sin θ = a K(k, k sin θ dθ = ae(k. I(a, b = K(k, J(a, b = ae(k. (9 a 5. I ( a + b, ab = I(a, b. 5

[ ] b tan θ = u du dθ = dθ cos θ du = cos θ b cos θ = cos θ b I(a, b = = I = b + u. dθ a cos θ + b sin θ = (a + u (b + u du = ( a + b, ab = b cos θ, cos θ = + tan θ = (( a+b dθ cos θ a + b tan θ b b + u, (a + u (b + u du. + u (ab + u u = ( v ab ab + u = v 4v (ab + v du, ab + u dv = v, ( a + b + u = 4 (a + v ( + b v = 4v (a + v (b + v v u ( a + b I, ab = dv = I(a, b. (a + v (b + v du. 6. k = k K(k = π M(, k. [ ] a =, b = k n =,,... a n+ = a n + b n, b n+ = an b n m = M(, k lim a n = lim b n = m n n 5 I(, k = I(a, b = = I(a n, b n n K(k = I(, k = I(m, m = m dθ = π m = π M(, k. ( a + b J, ab J(a, b. de dk = dk (E K, k dk = kk (E k K. 6

. (a K(k = + k K (c E(k = + k E 7. [ ] J ( k + k ( k + k J k = b a, k = ( a + b, ab = a + b E, (b K(k = + k K + k K(k, (d E(k = ( + k E ( a + b, ab J(a, b = abi(a, b. b a, k = a b + k a + b ( 4ab (a + b, + k ( k k K(k. + k ( k J(a, b = ae(k = a + b E ( a b. a + b J(a, b = ae(k I(a, b = K(k (d a ( a + b J, ( a b ab J(a, b = (a + be ae(k a + b ( k = (a + be ae(k + k ( k = (a + b E(k + + k + k K(k ae(k = bk(k = abi(a, b. 3. lim n n c n =. [ ] (7 8. [ ] ( J(a, b = a n c n I(a, b. n= A n = n (J(a n, b n a ni(a n, b n 7 5 A n+ A n = n (J(a n+, b n+ J(a n, b n n+ a n+i(a n+, b n+ + n a ni(a n, b n = n a n b n I(a n, b n n+ a n+i(a n, b n + n a ni(a n, b n = ( n a n b n (a n + b n + an I(an, b n = n (a n b ni(a n, b n = n c ni(a, b. 7

n A n = a ni(a n, b n J(a n, b n = = = c n a n a n cos θ + b n sin θ dθ a n a n cos θ b n sin θ a n cos θ + b n sin θ dθ = sin θ a n cos θ + b n sin θ dθ c n a n cos θ + b n sin θ dθ (a n b n sin θ a n cos θ + b n sin θ dθ dθ a n cos θ + b n sin θ = c ni(a n, b n. < A n n c ni(a n, b n = n c ni(a, b. 3 lim n n c n = A + n= (A n+ A n = lim N A N+ =. J(a, b a I(a, b = A = (A n+ A n = n c ni(a, b J(a, b = = I(a, b ( a n= n c n, n= n c n I(a, b. n= n= 9 (. E(kK(k + E(k K(k K(kK(k = π. [ ] a =, b = k = k = 9 E ( ( ( K K = π. 8 E ( ( = n c n K n= (. 8

( 6 ( K n c n K n= ( = M n c n 4M n= ( = π. π (, π (, = π. C 3. a, b, c C c n Z, n a (n = a(a + (a + n (a + n, a ( = F (a, b, c; u = n= a (n b (n n!c (n un (. f(u = F (a, b, c; u u < u( u d f df + (c (a + b + u abf = ( du du ( x / K(k. K(k = π F (,, ; k. 4. K (k = K(k K(k, K (k (k 3 k d y dk + (3k dy + ky = ( dk 9

K K ( 5. K (k = K(k, E (k = E(k EK + E K KK [ ] 5 W = EK + E K KK lim W K( = π k E( = W = (E KK + E K sin θ dθ = cos θ dθ = [ sin θ ] π =. lim W = lim (E k k KK + E(K( = lim (E KK + π k. lim k (E KK = (K EK = = k ( ( = kk kk ( dθ k sin θ ( k sin π θ k sin θ dθ ( k sin θ dθ k dθ cos θ + k sin θ k dθ k cos θ + k sin θ = kk π k sin θ dθ K(k dθ ( k sin θ k dθ ( k sin θ < (K EK < kk π (k. [] π. [],,, 999. [3] π 7 3