高校生の就職への数学II

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.......................................................................................... 3..3............................... 9............................ 0.............................. 0............................. 4............................ 4........................... 4............................ 8..3........................................................... 7........................ 7.............................. 3 35 3................................... 35 3.............................. 35 3.............................. 37 3..3........................... 40 3..4........................... 4 3...................................... 46 3.............................. 46 3................................ 50 3.3................................ 54 3.3............................ 54 3.3.......................... 55 60 4................................... 60 4................................ 60 4........................ 6 iii

4..3.......................... 66 4..4............... 67 4................................... 70 4......................... 70 4............................ 73 77 5................................... 77 5.............................. 77 5................................ 80 5................................... 85 5............................ 85 5................................ 90 5..3.............................. 94 97 6.............................. 97 6................................ 97 6........................... 0 6..3........................... 04 6............................... 07 6....................... 07 6...................... 6.3................................... 5 6.3............................... 5 6.3................................ 8 6.3.3....................... 9 (.................................. 9 (.............................. 3 (................................ 34 (.................................. 36 (............................ 40 (................................. 4 46 iv

... A B A B. 3 5 + 9 3 + + 3 3 5 +9 3 + 3 +9 4 +6 +3 ( + 3. ( ( 6 + 3 ( ( ( ( 3 + 3 + + 4 ( + ( (3 ( 3 + 3 ( 3 ( (4 (3 3 4 + ( ( (5 (p 3 + p 4p 4 (p ( (6 ( 3 + + 3 ( + ( (7 (8 3 8 + 8 (4 3 + ( (8 (8a + a 3 a 4 a + 3 (3 a a (JFE (9 ( 3 3 + 8 3 ( (JFE

A B Q R Q A = BQ + R B A R R 0 B. 3 3 4 + 6 + 8 B 3 + + B +3 3 3 4 3 + 3 + 6 + 8 = B (3 + + + 3 4 +5 +6 3 3 + 6 +5 3 3 4 + 5 + 6 = B (3 + 6 4 9 +6 3 3 4 + 5 + 6 3 + 9 +6 B 0 B = + 3. A B ( A 3 + ( 3 7 + 8 + B 3 + 5

3.. C 0 A B = A C B C. ( 5a b 5 3b 5a 0a 3 b = b 3 3 a 5a b 3 = 3b a A C B C = A B ( + 3 = ( + 3 ( ( + ( = + 3 +..3 ( 54a 0 b 6 c 8 6a 4 b cd ( ( 3 + ( (3 + 3 + + ( (4 + 6 6 + 4 ( (5 ( + 3 + ( + ( + ( + ( 3 ( (6 a + b a b b + a b a (

4.3 ( A B C D = AC BD A B C D = A B D C = AD = ( + ( ( = ( + BC ( 7 + + 5 ( ( 3( + 5 = + 5 ( 3( 4 ( + 5 = ( ( 3( + 5 ( 3( 4 ( + 5 = 4.4 ( 3 4a b 3 8a3 b 9 3 ( ( 4 5 3 3 3 3 ( ( (3 5a a 6 (NOK 9 (4 ( ab ( ( a b 3 ( (5 3 4 ( (6 + ( (7 + 4 (

5.5 ( 3 + 36 6 9 + 4 ( ( 4 6 8 + 4 + 4 ( (3 a a + 30 a 6a + 9 a 3a a 5a ( (4 3 4 + 4 + 4 4 + 3 ( (5 3 + 9 6 + 8 5 3 ( (6 + + + ( (7 9 + 6 + 9 + 3 6 ( (8 3 3 3 8 + + + 4 ( (9 6 5 6 7 0 3 + 7 + 4 4 + (

6. ( 3 + + ( 3 3 + 3 4 ( 3 + + = 3 + + ( = = ( = (3 ( + = ( 3 3 + 3 4 = 3 ( ( 3 ( + ( = ( 3( + ( ( + ( (3 ( ( ( + ( = ( + 6 (3 5 + ( ( + ( = = + 6 8 ( ( + ( ( ( 4 ( ( + ( = 4 ( ( +.6 ( a a b + b b a ( ( 3 + + 3 ( (3 + ( (4 + 4 3 ( + ( ( (5 a a + a + a a + a (

7.7 ( 4 ( ( 4 8 6 ( (3 + + (NEC (4 + 8 ( 4 (5 + + ( (6 + + + ( (7 + ( (8 + b a b ( (9 + (

8.8 ( a + b ab b + c bc a + c ac ( ( 3 + ( (3 4 + 3 4 + 5 + 3 + 4 5 ( (4 a + (a + (a + + (a + (a + (a + 3 ( (5 a + (a + (a + (a + (a + 3 ( (6 + + 5 3 + 3 ( (7 5 + 3 + 3 + 6 5 + (JR (8 + 5 + + + 5 + 3 + 3 + 3 + 3 (

9..3 a + b + c = a + b + c a = a, b = b, c = c a + b + c = 0 a = b = c = 0.3 a( + + b( + c( + ( = + 3 a b c (a + b + c + (a b c = + 3 a + b + c = a b = 0 c = 3 a = b = c = 3.9 ( A( ( + 3 + B( + C = 3 + 5 A, B, C ( ( = a + b + a, b ( (3 A, B, C ( 3 9 ( ( = A + B + + C

0....4 a + b + c = 0 a b = bc + c c = a b a b (bc + c = a b b( a b ( a b = a b + ab + b (a + ab + b = 0 a b = bc + c.0 a + b + c = 0 ( (a + b(b + c(c + a + abc = 0. a + b + c = 0 ( a ( b + c + b ( c + a + c ( a + b + 3 = 0

.5 a b = c d a + 3c b + 3d = a 3c b 3d a b = c d = k a = bk c = dk a + 3c b + 3d a 3c b 3d a + 3c b + 3d = bk + 3dk b + 3d = bk 3dk b 3d = a 3c b 3d = k(b + 3d b + 3d = k = k(b 3d b 3d = k. a b = c d ( ab + cd ab cd = a + c a c.3 a = b (JFE ( a = + a ab + b ( pa + r qa + s = pb + r qb + s

.. a a 0 a = 0 a b a + b 0 a = 0 b = 0.6 a + b 4(a b a + b 4(a b = a 4a + 4 + b + 4b + 4 = (a + (b + 0 a + b 4(a b a = 0 b + = 0 a = b =.4 ( a + b (a + b ( ( a ab + b 0 ( (3 + + z + z + z (

3 a + b a b a b a > 0 b > 0 ab a b a > 0 b > 0 a + b ab a = b a + b ab.4 a > 0 a + 9 a 6 a > 0 9 a > 0 a + 9 a a 9 a = 9 = 6 a + 9 a 6.5 ( a > 0 a + a ( ( ( a > 0, b > 0 (a + b a + 4 b ( ( a (3 a > 0, b > 0, c > 0, d > 0 b + c ( b d a + d 4 c (

4... i i a b a + bi 3 a b c d a + bi = c + di a = c b = d a + bi = 0 a = 0 b = 0. a b (3 + ia ( ib = + 4i (3a b + (a + bi = + 4i ( 3a b a + b 3a b = a + b = 4 a = b =. ( 3 + ( 3i = 7 i ( ( ( + 5i + (7 i = 5 i ( (3 ( i + ( + i = 4 (

5. ( (3 + i + (4 3i ( ( + i(3 i (3 (3 + i (4 ( + 3i( 3i ( (3 + i + (4 3i = (3 + 4 + ( 3i = 7 i ( ( + i(3 i = 3 i + 6i 4i (3 (3 + i = 9 + i + 4i = {3 4 ( } + ( + 6i = 7 + 4i = {9 + 4 ( } + i = 5 + i (4 ( + 3i( 3i = (3i = 4 9i = 4 9 ( = 3. ( (4 + 3i( + i ( ( ( + 3i(4 i ( (3 (4 3i(3 + 5i (NEC (4 (5 3i(4 + i ( (5 (4 i(4 + i ( (6 (3 i(6 + 4i ( (7 ( i 3 ( (8 5i 3 5i 5 ( (9 i i + i 3 i 4 + i 5 ( (0 ( + i i 3 ( ( ( 7 3 i( 7 + 3 i ( ( ( + 3 i(3 7 i ( (3 ( + i 3 ( (4 ( + 3 i 3 (

6 a + bi a bi.3 4 + 3i 3i 4 + 3i (4 + 3i( + 3i = 3i ( 3i( + 3i = 5 + 5i 0 = + 3 i = 4 + i + 3i + 9i + 3.3 i a + bi ( 4 3i.4 ( + 3i 4i ( + i i (3 + i + i (4 i + i (5 i 3i (6 3i 3 + i (7 + i i (8 (9 ( i( + 3i + i (3 i(4 + 3i 3 + i (0 i + i + i + + i + i ( ( ( ( ( ( ( ( ( (NEC

7 a > 0 a = a i = i.4 a ± a = ± a i ( 4 ( 4 9 (3 = 5 ( ± 4 = ± 4 i = ± 6 i ( 4 9 = i 3i = 6i = 6 (3 = ± 5 = ± 5 i (4 ( = 4 = ± 4 = ± i (4 ( = 4.5 ( 4 5 ( ( 8 ( (3 ( + ( (JFE (4 ( 8 + 6 (.6 (t 3 + 9 = 0 (

8.. a + b + c = 0 I b 4ac.5 a + b + c = 0 = b ± b 4ac a ( 3 + 4 + = 0 ( 6 + 5 = 0 ( = 4 ± 4 4 3 3 = 4 ± i 6 = 4 ± 8 6 = ± i 3 ( = ( 6 ± ( 6 4 5 = 6 ± i 4 = 3 ± i = 6 ± 4 4.7 ( 5 + 4 + 7 = 0 ( ( 3 + 5 + = 0 ( (3 3 = 3 ( + ( 4

a +b+c = 0 = b ± b 4ac a b 4ac b 4ac a + b + c = 0 D a + b + c = 0 D D > 0 D = 0 ( 9 D 0.6 D < 0 ( + 3 = 0 D = 4 ( 3 = 5 > 0 ( 9 + 4 = 0 D = ( 4 9 4 = 0 (3 3 + 4 = 0 D = ( 3 4 4 = 3 < 0.8 ( = 0 ( ( 4 5 = 0 ( (3 4 + 9 = 0 ( (4 + + = 0 ( (5 + 4 + 3 = 0 ( (6 4 m + 9m = 0 (m (

0. ( + a a + 3 = 0 a ( ( + k + 8k + 9 = 0 k ( (3 (a + + 4 = 0 a ( (4 + 6 + k + = 0 k ( ( + a a + 3 = 0 D = a 4 ( a + 3 = a + 4a = (a + 6(a D > 0 (a + 6(a > 0 a < 6 < a ( + k + 8k + 9 = 0 D = (k 4 (8k + 9 = 4(k 8k 9 = 4(k + (k 9 D = 0 (k + (k 9 = 0 k = 9 (3 (a + + 4 = 0 D = { (a + } 4 4 = a + 4a = (a + 6(a D < 0 (a + 6(a < 0 6 < a < (4 + 6 + k + = 0 D = 6 4 (k + = 8k + 3 D 0 8k + 3 0 k 4

.9 ( 4 + (k + = 0 k ( ( (k 4 + k = 0 k ( (3 + a + a 3 = 0 a ( (4 k k k + = 0 k ( (5 + 6 + k = 0 k ( (6 + 4 m 5m = 0 m + m 6 = 0 m (

..3 a + b + c = 0 α β α + β = b a, αβ = c a.7 3 + 6 = 0 α β α + β = 3, 6 αβ = 3 =.0 ( + 3 = 0 (NTT ( 3 + 5 = 0 ( (3 3 + 4 = 0 (. + 3 + 4 = 0 α β ( α + β ( α 3 + β 3 (3 (α β (4 α β + β α α + β = 3 αβ = 4 ( α + β = (α + β αβ = ( 3 4 = ( α 3 + β 3 = (α + β 3 3αβ(α + β = ( 3 3 3 4 ( 3 = 9 (3 (α β = (α + β 4αβ = ( 3 4 4 = 7 (4 α β + β α = α αβ + β αβ = α + β αβ = 4

3. ( + 4 + = 0 α, β (NTT (i α + β (ii αβ (iii α + β ( 3 + 5 + = 0 α, β ( (i α + β (ii αβ (iii α + β (3 + = 0 α, β ( (i α + β (ii αβ (iii α + β (iv (α β (4 + = 0 α, β α + β ( (5 3 + 4 = 0 α, β (i α β + αβ (ii α + β ( (6 4 + + 5 = 0 α, β ( (i (α + β 4 (ii (α β 4 (7 + 6 = 0 α, β α + α β (NTT ( (8 3+5 = 0 α, β β + α ( β β α + α ( β

4.3 + 7 + m = 0 m ( 3 : 4 ( 3 ( 3α 4α 3α + 4α = 7 3α 4α = m 7α = 7 α = m α = m = ( = 3α = 3( = 3 4α = 4( = 4 ( m = 3 4 ( α α + 3 α + (α + 3 = 7 α(α + 3 = m α + 3 = 7 α(α + 3 = m α = 5 m = 5( 5 + 3 = 0 α + 3 α + 3 = 5 + 3 = ( m = 0 5. ( + 3 + k = 0 k ( ( m + m + = 0 m (JFE (3 + a + 4 a = 0 : 3 a (

5.4 + p + q = 0 3 + 7 p q 3 7 3 + 7 p = 6 q = + 3 7 = p 3 + 7 3 7 = q.3 ( + p + q = 0 5 p, q ( ( + a b = 0 3 + 5 3 5 a b ( α β α β (α + β + αβ = 0 p q p + q = 0.8 3 + i 3 i (3 + i + (3 i = 6 (3 + i(3 i = 9 4i = 3 6 + 3 = 0.4 3 (

6.5 3 + 5 = 0 α β α + β + 3 + 5 = 0 α + β = 3 αβ = 5 (α + + (β + = (α + β + 4 = 3 + 4 = 7 (α + (β + = αβ + (α + β + 4 = 5 + 3 + 4 = 5 α + β + 7 + 5 = 0.5 ( 5 4 = 0 α, β α, β ( ( 7 + 5 = 0 α, β ( (i α β (ii α β (3 3 4 + 5 = 0 α, β α + β, α + β (

7... P ( k P (k ( P ( a + b P b a.9 ( P ( = 3 + 3 P ( P ( = 3 + 3 = ( P ( = 3 + 5 + + 4 + P ( P ( = ( 3 + 5 ( + ( + 4 = 6.6 ( 3 + 5 4 + 3 ( ( 3 + 3 ( (3 8 4 6 7 + 3 (

8.6 3 m + 4 + m (NTT P ( = 3 m + 4 P ( = 0 ( 3 m ( + 4 = 0 m =.7 ( 3 a + + a (NTT ( 3 + p + + 6 3 p ( (3 4 p 3 + p 4 + p ( (4 3 p + + 4 p p (

9.7 3 + a + + b + a b P ( = 3 + a + + b + = ( ( + P ( ( ( + P ( = 0 P ( = 0 P ( = 0 3 + a + + b = 0 a + b = P ( = 0 ( 3 + a ( + ( + b = 0 4a + b = 0 a = 4 b = 6.8 ( 3 + 3 + a + b + 3 5 a b ( ( 3 + p + q 5 p q (NHK (3 3 + a + b 8 + 6 a b (

30.8 P ( + 7 5 P ( ( ( + P ( ( ( + a + b Q( P ( = ( ( + Q( + a + b P ( = a + b P ( = a + b 7 P ( = 7 + 5 P ( = 5 a + b = 7 a + b = 5 a = 4 b = 4 +.9 ( 3 5 6 ( ( 5 ( ( f( + 3 + + f( ( ( + (

3 P ( k P (k = 0.0 3 + 3 5 6 P ( = 3 + 3 5 6 P ( = ( 3 + 3 ( 5 ( 6 = 0 + 6 + 3 +3 5 6 P ( + 3 + 5 3 + 3 5 6 = ( + ( + 6 + 6 6 6 6 3 + 3 5 6 = ( + ( + ( 3 0.0 ( 3 3 + (JFE ( 3 3 ( (3 3 3 + + ( (4 3 4 + 5 ( (5 3 6 + 7 ( (6 3 + 5 6 ( (7 3 5 + 6 ( (8 3 4 8 + 8 ( (9 3 + 5 4 ( (0 3 3 + 6 ( ( 3 3 5 4 + 4 ( ( 4 3 7 + + 6 (

3... ( 3 + 8 = 0 ( 4 + 3 4 = 0 (3 ( + ( + 3 = 0 ( 3 + 8 = 0 ( + ( + 4 = 0 + = 0 + 4 = 0 = ± 3 i ( 4 + 3 4 = 0 ( ( + 4 = 0 = 0 = ± ±i + 4 = 0 (3 + = X X X 3 = 0 (X + (X 3 = 0 ( + + ( + 3 = 0 ( + ( ( + 3 = 0 = ( 3. ( 3 = 0 ( ( 4 3 4 = 0 ( (3 4 + 8 = 0 ( (4 4 + 9 = 0 ( (5 ( 3 ( 3 8 = 0 ( (6 ( 3 8( 3 0 = 0 ( (7 ( + ( + ( 5( 6 = 44 (

33.9 3 + 4 + 3 = 0 P ( = 3 + 4 + 3 ( P ( = ( 3 + 4 ( + 3 ( = 0 P ( + P ( = ( + ( + P ( = 0 + = 0 + = 0 = ±. ( 3 3 + = 0 ( ( 3 6 + 4 = 0 ( (3 3 4 + 5 = 0 ( (4 3 5 + 6 = 0 ( (5 3 6 + 6 = 0 ( (6 3 8 + 7 0 = 0 (TDK (7 3 + + + 6 = 0 (NEC (8 3 3 3 + 3 3 = 0 (

34.0 3 + 4 + a + b = 0 3 ( a b ( ( 3 3 + 4 + a + b = 0 ( 3 3 + 4 ( 3 + a ( 3 + b = 0 a + b + 5 = 0 3a + b + 9 = 0 a = b = 6 ( ( 3 + 4 + 6 = 0 ( ( + 3( + = 0.3 3 + a + 5 = 0 ( ( a ( (.4 4 + 3 + a + b = 0, a, b (

35 3. 3.. A(a B(b AB AB = b a m n A P B A(a B(b AB m : n P Q m < n n na + mb P Q m A B m + n m > n na + mb m Q n m n A B Q a + b 3. ( O A(5 ( A(4 B( 3 ( OA = 5 = 5 ( AB = 3 4 = 7 = 7 3. ( O A( 3 ( A( B(7 (3 A(6 B( 4

36 3. A( B(6 AB ( 3 : P 3 : 4 Q (3 M ( P + 3 6 = 0 3 + 5 = 4 ( Q 4 + 3 6 3 4 (3 M + 6 = 7 = 4 = 4 3. A( B(6 AB ( 3 : 5 P ( : Q (3 3 : 7 R (4 M

37 3.. A(, B(, AB AB = ( + ( O A(, OA OA = + 3.3 A(, 3 B(5, AB AB = (5 + { ( 3} = 3 + 4 = 5 = 5 O A( 4, OA OA = ( 4 + ( = 0 = 5 3.3 ( A(7, 5 B(4, ( ( A( 3, B(3, 6 ( (3 A(, 0 B(0, 6 ( (4 A(8, 7 B( 4, ( 3.4 3 A(5, B(, 3 C(0, 3 ABC 3 (

38 3.5 ABC ( A(6, 5 B(5, 0 C(, 4 ( ( A(, B(, C(5, 3 ( 3. A(3, B(, 6 P P P (0, PA = PB PA = PB (3 0 + ( = ( 0 + (6 0 = 30 P (0, 3 = 3 3.6 A(, B(6, 3 C (

39 A(, B(, AB m : n P Q ( n + m P m + n, n ( + m n + m Q, n + m m + n m n m n ( + AB, + 3.4 A(8, 7 B(, 8 AB : P ( 8 + +, 7 + ( 8 (6, + 3 : Q ( 8 + 3 7 + 3 ( 8, ( 0, 38 3 3 3.7 ( A(3, B(8, 5 AB 3 : ( ( A( 4, 0 B(0, 3 AC B C ( (3 A( 7, 0 B(3, 5 AB 3 : C AB ( (4 A(, 3 B(5, 0 ( (i AB (ii AB : (iii AB : 4

40 3..3 ( (, m = m( 3.5 (, 5 3 ( 5 = 3( = 3 3.8 ( (, 5 3 ( ( (0, ( (3 (0, 3 ( (4 (, ( (5 3 (, 5 ( (6 (5, 60 (

4 ( (, (, = ( = = 3.6 (, 4 (, 7 ( 4 = 7 4 ( = 3 + 3.9 ( (, 3, (5, 0 ( ( (, 5, (4, (NTT (3 (, 3, (5, 7 ( (4 (4, 5, (, 7 ( (5 (0, (, ( 3.0 ( ( ( (3 (, 6 ( 3, 5 (3, 4 O O 4 O 5

4 3..4 = m + k = m + k m = m m m = 3. ( ( = 3 5 ( 3 + = 5 (3 3 5 = 8 (4 3 = 5 (5 6 = + 7 (6 = 3 3. ( (, 3 = + 3 ( ( A( 4, B(4, 5 P(3, 4 ( (3 (3, = 4 ( (4 (, + 4 + 8 = 0 ( (5 + 3 3 = 0 (4, 6 ( (6 (, 5 ( 3, 3, (, 5 ( 3.3 m 7 = 0, (m 3 + 5 = 0 m m (

43 3. A(, 3 B(4, AB AB M ( + 4, 3 + ( (3, AB 3 4 = AB m m = m = O A(, 3 M B(4, = ( 3 = 0 3.4 ( A B (0,, (4, AB ( ( A(, 0 B(4, 3 (NTT

44 3.3 + = 0 l l A(, B B (s, t l AB t s AB l t s = B(s, t A(, s + t 4 = 0 ( s + AB, t + l s + t + s t + 7 = 0 + = 0 s = t = 3 B (, 3 l 3.5 3 + = 0 l l A(, 5 B

45 3.4 (3k + (4k + 5k 4 = 0 k k k k (3 4 + 5k + ( + 4 = 0 k 3 4 + 5 = 0, + 4 = 0 = = (, 3.6 ( k + ( k = 0 k ( ( = m + (3m + m ( (, a + b + c = 0 d d = a + b + c a + b 3.7 (, 4 + 3 = 0 d d = 4 + 3 4 + 3 = 0 5 = 0 5 = 3.7 ( 4 5 = 0 (NTT ( (5, 3, (, (NTT

46 3. 3.. (a, b r ( a + ( b = r r + = r 3.8 ( (, 3 ( ( (, 4 ( (3 (, 5 ( (4 (3, 0 (NHK (5 (3, 4 (7, 7 ( (6 (3, 4 (

3.5 A(3, 4 B(5, C r C AB A(3, 4 ( 3 + 5, 4 + ( (4, C r = CA = (3 4 + (4 = O 0 47 ( 4 + ( = ( 0 B(5, ( 4 + ( = 0 3.9 ( A( 3, 4 B(5, AB ( ( (3,, (, 5 ( (3 (, 3, (4, 5 (

48 3.8 + + 4 0 = 0 ( + + + ( 4 + 4 = 0 + + 4 ( + + ( = 5 (, 5 3.0 ( + 8 4 + = 0 (JFE ( + + 6 6 = 0 ( (3 + 6 = 0 ( (4 + + 4 3 = 0 ( (5 + + 4 6 + = 0 ( (6 + 4 + + = 0 ( (7 + + 4 = 0 ( (8 + = + ( 3. + 4 + 0 = 0 (4, (

49 3.6 3 A(, 7 B(, C(6, 0 + + l + m + n = 0 A ( + 7 l + 7m + n = 0 B + ( + l m + n = 0 C 6 + 6l + n = 0 l + 7m + n + 50 = 0 l m + n + 8 = 0 6l + n + 36 = 0 l = 4 m = 6 n = + 4 6 = 0 3. 3 ( (0, 0, (3,, (, ( ( (3, 5, (3,, (4, 0 (

50 3.. 3.7 + = 0 = { + = 0 + =0 = 0 + ( = 0 3 = 0 =, 3 0 = = = 3 = 3 = (, 3 (3, O 0 0 3.3 ( + = 5 + = 0 ( ( ( + = 5, = 5 (3 + = ( (4 + = + = ( (5 ( + ( = 8 + = 3 (

5 ( a +b+c = 0 D = b 4ac D D > 0 D = 0 D < 0 a + b + c = 0 ( 0 3.8 + = 5 = m+5 m + = 5 = m + 5 (m + + 0m + 0 = 0 D = (0m 4 (m + 0 = 0(m 4 D = 0 m 4 = 0 m = ± 3.4 ( + = 4 60 (NEC ( + 6 + 8 = 0 ( (3 + 0 + 8 = 0 (

5 ( O r l O l d d r d < r d = r d > r l l r r d d O O l d r O 3.9 + = 9 4 + 3 + k = 0 k r 3 4 + 3 + k = 0 d d = 4 0 + 3 0 + k 4 + 3 = k 5 d = r k 5 = 3 k = ±5 3.5 ( 3 + 4 = a + = a ( ( + = = c c (

53 + = r P(a, b a + b = r 3.0 A(, + = P(a, b P a + b = P a + b = A(, a + b = a O 5b 4b = 0 4 b = 0, 5 + = A(, b = 0 a =, b = 4 5 a = 3 5 (, 0 + 0 = = ( 3 5, 4 3 5 5 + 4 5 = 3 + 4 = 5 3.6 ( (3, + = 5 ( ( (3, + = (

54 3.3 3.3. P (, P P 3. A(, 0 B(4, 0 : P P (, P AP : BP = : BP = AP 4BP = AP AP = (+ +, BP = ( 4 + 4{( 4 + } = ( + + + + 0 = 0 ( 6 + = 4 A O B 4 P(, P ( 6 + = 4 P(, (6, 0 4 3.7 O A(5, 0 3 : P

3.3. = m + k l > m + k 55 l > m + k l < m + k l m + k m + k l + < r + = r + > r + = r + r + r + = r r r O O + < r r < m + k + > r 3. { + > 6 + 3 + 3 > 0 + = 6 = 3 3 4 O 4 4 4 r

56 3.8 ( ( A(4, 4 O B(6, 0 ( ( O (3 ( (i (ii 5 O 4 4 ( 4, 3 O (4, 3 5 (4 ( (i (ii O

3.9 ( < 4 < 4 + 3 > 57 ( ( + 4 (JFE (3 < + < 4 ( (4 { + ( (5 { 3 3 ( (6 { + 4 (

58 3.3 ( + (3 > 0 ( + (3 > 0 { + > 0 3 > 0 { + < 0 3 < 0 O 3.30 ( ( ( < 0 ( ( ( + 4( + < 0 ( (3 ( + 4( > 0 ( 3.3 (, (. 0 +. 0 +. ( 0 + ( 0 + O. ( + 0

59 3.4 4 0, 0, + 3 5, 3 + 8 + A A 4 ( ( 8 (0, 0 3, 0 5 4 (, 0, 3 5 (, 3 A + = k O 8 5 3 A k (0, 0 k = 0 (, k = 3 ( 8 3, 0 ( 0, A 0 < k < 3 + = = 3 = 0 = 0 0 5 3 k = 8 3 k = 5 3 3.3 4 0, 0, 3 + 9, + 8 +

60 4. 4.. θ θ OX θ OP θ 4. 60 45 40 P 60 O X O 45 X P O P 40 X 4. ( 5 ( 70 (3 660 OP OX α OP α + 360 n 4. 330 390 690 30 330 690 30 390 = 30 + 360 330 = 30 + 360 ( 690 = 30 + 360 ( 390 330 690 O 330 390 30 P X 4. 480 840 40 480 840 0

6 ( 80 80 π π 4.3 35 π 80 35 = 3 4 π 4.3 ( 5 ( 60 (3 8 5 π (4 5 π r θ( l S l = rθ, S = r θ S = lr π 4.4 8 4 8 π = π 4 8 π 4 = 8π 4.4 l S π ( 8 ( 0 8 5 π

6 4.. θ r P(, P(, r sin θ = r ( θ r cos θ = r O ( r r tan θ = ( r 4.5 π 3 r = = = 3 ( sin π = 3 3 = 3 ( cos π = 3 ( tan π = 3 = 3 3 O 3 π 3 3 4.5 ( tan 0 ( ( sin( 0 ( (3 cos 960 (NTT (4 cos( 70 ( (5 sin π 6 cos 5 6 π ( (6 sin 45 cos( 300 + sin 50 cos 405 (

63 = sin θ π α π π O α π 3 π π π 5 π 3π θ = cos θ π α π π O α π π π 3 π 5 π 3π θ = tan θ π θ = π θ = 3 π α π π O α π π 3 π π 5 π θ

64 ( 4.6 = cos θ = cos θ + π 3 O π π θ ( = cos θ + π = cos θ θ π 3 3 O π π θ 4.6 ( ( = sin π ( ( ( = cos π 6 (

4.7 = cos θ = cos θ θ π 65 π π O π π 3 3π π 5 7 π θ 4.7 = sin θ ( = 3 sin θ O π π θ ( = sin 3θ O π θ

66 4..3 tan θ = sin θ cos θ 3 + tan θ = cos θ sin θ + cos θ = 4. θ 4 sin θ = 4 5 cos θ tan θ cos θ = sin θ = ( 4 = 9 5 5 θ 4 cos θ > 0 9 cos θ = 5 = 3 5 tan θ = sin θ ( cos θ = 4 3 5 5 = 4 3 4.8 ( θ 4 cos θ = 3 sin θ (NTT ( θ 3 cos θ = 3 4 sin θ tan θ ( (3 θ sin θ = 3 5 cos θ tan θ ( (4 θ 3 sin θ = 3 5 cos θ tan θ (

4..4 4. 67 ( cos θ = (0 θ < π ( tan θ = 3 ( θ 0 θ < π θ = 3 π, 4 3 π 4 π 3 O π 3 ( θ = 3 0 θ < π θ = 3 π θ = 3 π + nπ (n O 3 θ 3 cos θ = θ = 3 π + nπ θ = 4 3 π + nπ (n 4.9 ( sin = (0 90 ( ( 3 3 tan = 0 (0 π ( (3 tan( 0 = 3 (0 360 ( (4 cos = (0 90 (

68 4.3 0 θ < π sin θ + 5 cos θ + = 0 ( cos θ + 5 cos θ + = 0 cos θ 5 cos θ 3 = 0 ( cos θ + (cos θ 3 = 0 cos θ cos θ + = 0 cos θ 3<0 0 θ < π cos θ = 4. θ = 3 π, 4 3 π 4.0 ( sin sin = 0 (0 360 ( ( sin θ + 3 sin θ = 0 (0 θ < π ( (3 cos θ + sin θ = (0 θ < 360 ( (4 cos θ + sin θ + = 0 (0 θ < 360 ( (5 cos + sin = (0 80 ( (6 sin + cos = 0 (0 < 360 ( (7 sin θ + 5 cos θ 4 = 0 (0 θ < 360 (

69 4.4 0 θ < π sin θ > 0 θ < π sin θ = θ θ = π 6, 5 6 π O π 6 < θ < 5 6 π 5 π 6 π 6 4. 0 π cos > ( 4. 0 π (NEC ( sin sin = 0 ( sin sin < 0 4.3 = 4 cos θ + sin θ 3 (

70 4. 4.. sin(α + β = sin α cos β + cos α sin β sin(α β = sin α cos β cos α sin β 3 cos(α + β = cos α cos β sin α sin β 4 cos(α β = cos α cos β + sin α sin β 4.8 cos 5 cos 5 = cos(45 30 = cos 45 cos 30 + sin 45 sin 30 = 3 + 3 + = = 6 + 4 4.4 ( sin 75 ( ( cos 75 ( (3 sin 5 ( (4 sin 65 ( (5 sin 5 + cos 45 ( (6 cos 75 sin 5 (

7 5 tan(α + β = 6 tan(α β = tan α + tan β tan α tan β tan α tan β + tan α tan β 4.9 tan 5 tan 5 = tan(60 45 = tan 60 tan 45 + tan 60 tan 45 3 = + 3 = ( 3 ( 3 + ( 3 = 3 3 + ( = 4 3 = 3 3 4.5 tan 75 ( 4.5 0 < α < π π < β < π cos α = 3 sin β = 3 cos(α+β 0 < α < π π < β < π sin α > 0 cos β < 0 sin α = ( 5 cos α = = 3 3 cos β = ( sin β = = 3 3 cos(α + β = cos α cos β sin α sin β = 3 ( 3 5 + 5 3 3 = 4 9 4.6 sin α =, sin β = 3 cos(α β 0 < α < 90 90 < β < 80 (

7 4.7 ( ( sin( + + sin( = sin cos ( ( sin 75 cos 5 4.8 ( sin(45 + α + sin(45 α = cos α ( ( sin A sin B = sin(a + B sin(a B ( 4.9 ABC B = 45 C = 60 BC = 0 AB ( 4.0 + p + q = 0 tan α, tan β tan(α + β p, q (

73 4.. sin α = sin α cos α cos α = cos α sin α cos α = sin α cos α = cos α cos α= sin α sin α= cos α 4.6 (sin α + cos α = + sin α = sin α + sin α cos α + cos α = (sin α + cos α + sin α cos α = + sin α cos α + sin α cos α = + sin α (sin α + cos α = + sin α sin α 4. + cos α = tan α ( 4. ( cos θ = 4 5 sin θ θ ( ( sin θ + cos θ = 6 sin θ (

74 sin α = cos α, cos α = + cos α 4.0 sin α = 0 < α < π cos α = 3 sin α cos α ( = α 3 3 cos = ( + = 3 3 sin α > 0 cos α > 0 sin α = 3 cos α = 6 3 4.3 π < α < 3 π cos α = 3 5 sin α cos α tan α = 4. tan α = 3 tan α = tan α tan α, α tan = cos α + cos α tan α tan α = 3 3 = 3 4 4.4 ( tan α = tan α ( π < α < π cos α = 4 5 tan α

75 4.7 0 θ < π cos θ + sin θ = ( sin θ + sin θ = sin θ(sin θ = 0 sin θ = 0 0 θ < π sin θ = 0 θ = 0, π sin θ = 0 sin θ = θ = π π θ = 0, π, 4.5 0 < π 3 sin cos = ( 4.6 = sin + cos (0 < π ( a sin θ + b cos θ a sin θ + b cos θ = a + b sin(θ + α cos α = a a + b, sin α = b a + b 4. r sin(θ + α π < α < π ( 3 sin θ + cos θ ( sin θ cos θ ( ( 3 sin θ + cos θ = sin θ + π 6 O π 6 P( 3, 3 ( sin θ cos θ = ( sin θ π 4 O π 4 P(,

76 4.8 0 < π sin + 3 cos = ( sin + π = 3 ( sin + π = 3 0 < π π 3 + π 3 < 7 3 π + π 3 = 3 4 π + π 3 = 9 4 π = 5 π, 3 π 4.7 ( 3 sin + cos = 3 (0 < 360 ( ( 3 sin θ cos θ = (0 < θ < 80 ( (3 3 cos θ sin θ = (0 θ < π ( 4.8 = cos sin (0 < π (

77 5. 5.. a 0 a`n a 0 n a 0 = a`n = a n a` = a 5. 3 0 = 5 = 5 0 = 0 = 00 5. ( ( ( 3 0 ( ( 3 ( 3 ( a 0 b 0 m n a m a n = a m+n am a n = am`n 3 (a m n = a mn 4 (ab n = a n b n 5. 3 6 3 4 = 3 6+( 4 = 3 = 9 ( 3 = ( ( 3 = 3 = 8 5. ( (3 3 3 3 ( 3 4 ( ( 5 3 (JFE

78 a > 0 b > 0 m n n a n b = n n a a ab n = n b b 3 ( n a m = n a m 4 m n a = mn a 5.3 3 5 3 5 = 3 5 5 = 3 5 3 = 5 ( 5 3 = 5 3 = 4 3 5 3 = 4 5 5.3 ( ( 6 4 3 ( ( ( 3 ( 7 a > 0 m n r a n = n a, a m n = ( n a m = n a m, a`r = a r 5.4 4 = 4 5 3 = 3 5 = 3 5 8 3 = 8 3 = ( 3 8 = = 4 5.4 a.5 ( 5.5 ( 7 3 ( 5 4 3 (3 5.5 (NTT ( ( (4 ( 5 4 ( 5.6 5.5, 8 5 4 (

79 ( a > 0 b > 0 r s a r a s = a r+s ar a s = ar`s 3 (a r s = a rs 4 (ab r = a r b r 5. ( 9 3 9 6 9 ( (8 6 4 (3 6 5 3 ( 9 3 9 6 9 = 9 3 + 6 = 9 = (3 = 3 ( = 3 = 3 ( (8 6 4 = 8 6 4 = 8 3 = ( 3 3 = 3 ( 3 = = = 4 (3 6 5 3 = 5 6 3 = 5 6 + 3 = = 5.7 ( 7 3 + (64 6 ( ( 8 8 5 3 8 3 ( (3 8 4 8 3 8 3 4 ( (4 (5 { ( } 3 3 9 4 6 ( ( 9 7 3 5 5 ( ( (6 ( 3 3 ( n a n = a (n 5.5 3 8 = 3 ( 3 = 5 = 5 ( 5 = 5.8 3 7 (

80 5.. = a a > a 0 < a < a O O (0, (, a a > 0 < a < 5.9 ( ( = ( = O O = a 3 a > r < s a r < a s 0 < a < r < s a r > a s

5.6 3 ( 3 5 ( ( ( 9 ( 3 3 3 ( 3 = 3 = 3 0 5 9 = 3 5 = 3 3 0 < 3 5 < 3 < 5 9 < 3 ( ( = 3 ( > 3 ( > 3 ( 3 5.0 3 ( 3 ( ( 0.5 4 ( 8 5. ( ( 3 ( < 8 ( 5 = 5 ( ( 3 ( < > 3 =( 5. ( 3 < ( 7 ( 3 8

8 5.3 ( 9 = 7 ( 8 = + ( 3 = 3 3 = 3 = 3 ( 3 = + 3 = + = 5. ( = 6 ( = 3 ( (KDDI (3 3 + = 7 (4 5 = 5 (5 5 +3 = 65 ( ( ( (6 ( 5 = 5 ( (7 4 3+ = 3 ( (8 3 = 9 (NTT (9 9 = 7 ( (0 36 = 6 6 + (

83 5.4 4 + 3 = 0 4 = ( + = 4 ( 4 3 = 0 ( + 4( 8 = 0 + 4 > 0 8 = 0 = 8 = 3 = X X 4X 3 = (X + 4(X 8 5.3 ( 4 + = 0 ( ( 4 + 8 = 9 ( (3 9 3 + = 3 3 ( (4 4 + 3 +3 + 3 = 0 ( (5 + + 3 = 0 ( (6 + + 3 = 5 +4 (

84 5.5 { 3 + 3 = 3 + = 7 3 = X 3 = Y 3 + = 3 3 = XY { X + Y = XY = 7 Y = X 3 3 > 0 3 > 0 X > 0 X > 0 0 < X < 4 3 X( X = 7 X X + 7 = 0 (X 3(X 9 = 0 4 X = 3, 9 3 { { { X = 3 Y = 9 X = 9 = Y = 3 { = = = 5.4 { + = 40 ( + = 56 ( ( { = 8 + 9 = 3 9 (

85 5. 5.. a > 0 a M > 0 M = a p log a M = p log a M a M M = a 0 a = a log a = 0 log a a = 5.7 ( log 36 = ( log = 5 ( log 36 = 36 = ( log = 5 = 5 > 0 = 6 = 3 5.5 ( log 6 = 3 ( ( log 8 = 4 5.8 ( log 5 5 ( log 6 log a M = p ( log 5 5 = log 5 5 3 = 3 ( log M = a p log a a p = p ( 4 6 = log = 4 ( 5.6 ( log 8 (NTT ( log 8 ( (3 log 0 (

86 5.9 ( log ( log 8 0 0.0 ( log 8 = log = log 3 3 = 3 ( log 0 0.0 = log 0 00 = log 0 0 = log 0 0 = 5.7 ( log 0 000 ( ( log 0 0. ( (3 log 0 0.00 ( (4 log ( (5 log 3 8 ( (6 log 0.5 0.5 ( (7 log cos 60 ( 5.8 ( log a = a log a a = 3 (a b 3 = a 3 3a b + 3ab b 3 4 D A + C B = AD AB + AC AB 5 A m A n = A mn

87 M > 0 N > 0 k log a MN = log a M + log a N log a M N = log a M log a N 3 log a M k = k log a M 5.0 ( log 6 9 + log 6 4 ( log 7 log 56 (3 log 0 5 log 0 5 + log 0 6 ( log 6 9 + log 6 4 = log 6 (9 4 = log 6 36 = log 6 6 = 7 ( log 7 log 56 = log 56 = log 8 = log 3 = 3 (3 log 0 5 log 0 5 + log 0 6 = log 0 5 log 0 5 + log 0 6 = log 0 5 6 5 5.9 = log 0 0 = ( log 8 + 3 log 3 8 ( ( log 0 5 + log 0 ( (3 log 4 log 3 (NTT (4 log 6 log 3 4 ( 3 (5 log 8 log 4 + log 6 ( (6 log 3 (4 7 + log 3 (4 + 7 ( (7 log 0 + log 0 5 log0 0.6 (NTT 4 (8 log 0 5 + log 0 5 ( (9 log 0 5 log 0 ( (0 log 0 3 + log 0 6 + log 0 5 (

88 0 log 0 5 log 5 5. log 5 + log 4 = log(5 4 = log 0 = 5.0 ( log 5 3 + log 5 log 8 3 ( ( log 45 3 log 3 + log 3 5 ( (3 log 5 3 log 9 4 + log 3 + log 8 ( a b c a c log a b = log c b log c a 5. log 3 8 = log 8 log 3 = log 3 log = 3 5 5 5. ( log 9 7 ( ( log 5 5 (NTT (3 log 8 ( (4 log 3 4 ( (5 log 00 0 0 ( (6 log ( 4 (7 log 3 9 (

89 5.3 log 3 log 4 7 = log 3 log 3 7 log 3 4 = log 3 3 log 3 = 3 5. ( log 3 log 8 9 ( ( log 3 log 3 5 log 5 7 log 7 8 ( (3 (log 3 + log 4 9(log 3 4 + log 9 (NTT 5.3 log 3 = a, log 3 = b log 44 66 a, b ( 5.4 log A =, log B =, log C = z,, z ( ( log A B ( log AB C (3 log C A B 5.4 ( 3 log 3 5 ( 5 3 log 5 log a M = p M = a p M = a log a M ( 3 log 3 5 = 5 ( 5 3 log 5 = 5 log 5 8 = 8 5.5 0 log (

90 5.. = a = = log a a > 0 < a < = a O a = a O a = = log a = = log a (, 0 (a, a > 0 < a < 5.6 ( = log ( = log 3 O O = log a a > 0 < p < q log a p < log a q 3 0 < a < 0 < p < q log a p > log a q

9 5.6 ( log 3 ( log ( 3 > ( log log 3 8 ( log ( 3 > log 0 < 3 < =log =log ( 3 3 < < 7 5.7 ( log 3 < ( log ( + 3 5.7 6 = ( 6 = 0 ( + ( 3 = 0 + > 0 3 = 0 = 3 = log 3 5.8 ( = 8 3 ( ( 4 + 3 + + 5 = 0 (

9 5.8 log + log ( 6 = 4 > 0 6 > 0 > 6 log ( 6 = 4 ( 6 = 4 ( + ( 8 = 0 + > 0 = 8 5.9 ( log 0 ( 3 = (NTT ( log( + + log 5 = ( (3 log 6 + log 6 ( 5 = ( (4 log + log( 3 = ( (5 log + log( 5 = ( (6 log( + + log( = ( (7 log( + + log( + 5 = ( (8 log( + + log( = 0 ( (9 log 0 3 log 0 4 + log 0 4 log 0 3 = ( (0 log( + log( 9 = ( ( log 0 (4 3 + log 0 (3 4 = ( ( log( + 6 = log( 4 ( (3 log( 5 = log( + 4 + log( 7 + log ( (4 log(4 + + log( + = ( log 3 + log 5 log 3 (KDDI (5 log( 3 6 + 7 log( = 0 ( (6 log ( 4 log 4 ( = 0 (

93 5.9 { 3 = log + log = = 3 > 0 3 > 0 > 3 log = log 0 = 0 (3 = 0 ( (3 + 5 = 0 3 + 5 > 0 = = 5 ( = = 5 5.30 { = 3 ( log + log = ( ( { + = 9 log + log = (KDDI (3 { log( + log(7 8 = log( 3 + 3 log( + = (

94 5..3 0 5.5 log 0 3.45 = 0.5378 ( log 0 34500 ( log 0 0.0345 ( log 0 34500 = log 0 (3.45 0 4 = log 0 3.45 + log 0 0 4 = 0.5378 + 4 = 4.5378 ( log 0 0.0345 = log 0 (3.45 0 = log 0 3.45 + log 0 0 = 0.5378 =.46 5.3 log 0 = 0.300 log 0 3 = 0.477 ( log 0 6 ( ( log 0 0 ( (3 log 60 ( (4 log 6000 ( (5 log 0 6 + log 0 ( (6 log 0 8 ( (7 log 6 ( (8 log.5 ( (9 log 0. ( (0 log 0.5 ( ( log.08 ( ( log 864 (NHK (3 log 5 (

5.3 log 8.5 = 0.994 ( ( log 85 ( log 850 (3 log 85 95 5.33 log = 0.300 ( ( log 0.5 4 ( log 0.4 5 5.0 log 0 = 0.300 log 0 3 = 0.477 6 30 log 0 6 30 = 30 log 0 6 = 30(log 0 + log 0 3 = 30(0.300 + 0.477 = 3.343 3 < log 0 6 30 < 4 log 0 0 3 < log 0 6 30 < log 0 0 4 0 3 < 6 30 < 0 4 6 30 4 5.34 ( 3 0 log 3 = 0.477 (KDDI ( 3 8 log 3 = 0.477 ( (3 log = 0.300, log 3 = 0.477 (

96 5. 0% 0 log 0 = 0.300 log 0 3 = 0.477 n 0. n 0 log 0. n log 0 0 3 n log 0 0 n( log 0 + log 0 3 log 0 + log 0 3 = 0.300 + 0.477 = 0.079 n log 0 + log 0 3 = 0.079 =.6 0 3 5.35 ( log =.0453, log 0 =.300 ( ( 0.08 log = 0.300, log 3 = 0.477 ( (3 50 49 000 log 7 = 0.845 log = 0.300 (

97 6. 6.. = f( a = f( b f(b B f(b f(a = b a f(b f(a f(a = a = b A f( b a AB O a b 6. f( = + = = 3 f(3 f( 3 ( = ( 3 + 3 { ( + ( } 3 ( = 5 5 = 3 6. = + 3 4 = = ( 6. lim ( + 3 lim ( + 3 = + 3 = 4 6. ( lim 3 3(5 ( ( lim ( (

98 6.3 3 + lim + 6 3 + lim + 6 = lim ( ( ( + 3( = lim + 3 = + 3 = 5 6.3 ( lim 3 9 3 ( lim (3 lim + 6 + (4 lim 0 + (5 lim + (6 lim 3 (7 lim 3 + 6 (8 lim 6 7 + 6 6.4 ( lim 3 4 8 3 ( lim h 0 (a + h 3 a 3 h ( (NEC ( ( ( ( ( ( ( (

99 6. a b + a + b lim 3 + = 5 lim ( + a + b = lim + a + b = 5 0 b = a 4 + a + b lim 3 + = lim { + a + b 3 + ( 3 + + a a 4 3 + = lim + a + = a + 4 } = lim ( ( + a + ( ( a + 4 = 5 a = b = 6 ( a = b = 6 6.5 a, b ( lim a + + b = 3 ( ( lim + a + b = 5 3 (

00 f( = a f 0 (a = lim h!0 f(a + h f(a h f(a + h = f( f(a A A = f( A(a, f(a O f( = a a a + h f (a 6.4 f( = = 3 f (3 = lim h 0 f(3 + h f(3 h 6h + h = lim h 0 h = lim h 0 (6 + h = 6 = lim h 0 h(6 + h h = lim h 0 (3 + h 3 h = (3, 9 f (3 = 6 6.6 f( = f (a (

0 6.. f 0 ( 6.5 f 0 ( = lim h!0 f( + h f( h f( = 5 ( f ( ( f 5( + h 5 ( = lim h 0 h = lim h 0 (0 + 5h = 0 ( f ( f ( = lim h 0 0h + 5h h ( f ( = 0 = 0 f ( = 0 ( = 0 = f( 0 d d 6.6 5 (5 d d (5 (5 = 0 d d (5 = 0 d d (3 f( = 3 6.7 f ( = lim h 0 ( + h 3 3 h = lim h 0 6 h + 6h + h 3 h d d (3 = 6 d d (53 = lim h 0 ( 3 + 3 h + 3h + h 3 3 h = lim h 0 (6 + 6h + h = 6 (

0 n n ( n 0 = n n` c (c 0 = 0 n =,, 3 ( = ( = ( 3 = 3 k = kf( 0 = kf 0 ( = f( + g( 0 = f 0 ( + g 0 ( 3 = f( g( 0 = f 0 ( g 0 ( 6.7 = 3 4 + 5 + 3 = ( 3 4( + 5( + (3 = 3 4 + 5 + 0 = 6 8 + 5 6.8 ( = 3 + 6 ( ( = 3 + 3 5 ( (3 f( = 3 4 + 4 + 5 ( (4 = 4 3 + + 9 ( 6.9 ( d d (4 + 3 + 3 + + 4 ( = 3 d + + 4 d ( (

03 6.8 = ( + 3 ( + 3 = ( + 6 + 9 = 3 + 6 + 9 = 3 + 6 + 9 = 3 + + 9 6.0 ( = (5 + 4( + ( ( = ( 3(3 ( (3 = ( 3 ( (4 = ( + ( 5 (NEC (5 f( = ( + ( 3 + 5 ( (6 = ( ( + + 4 ( (7 = ( ( + + ( (8 = ( + ( (9 = ( + 5(3 + ( + 4 ( 6. = (3 + d d (NEC 6. = ( f( = ( 3

04 6..3 = f( A(a, f(a f(a = f 0 (a( a 6. = 3 = l f( = 3 f ( = 3 f( = 3 = 3 f ( = 3 = l ( 3 = ( = 5 6.3 ( = 3 (3, 0 ( 3 O l ( = 3 3 + (, 4 ( (3 = 3 = ( 6.4 = 6 + (JFE ( A(5, 4 ( A (3

05 6.3 = 3 + 4 C(, = 3 + 4 = 3 (a, a 3a + 4 a 3 (a 3a + 4 = (a 3( a C(, (a 3a + 4 = (a 3( a a 4a + 3 = 0 (a (a 3 = 0 a =, 3 a = = ( a = 3 4 = 3( 3 ( = + 3 = 3 5 C O 4 6.5 (, 3 = (

06 6.6 = + 3 + (0, 3 ( 6.7 = + 3 (, 0 ( (0 (NEC (, 0 = + 3 A(a, a + 3 A f( = + 3 f ( = f(a = a + 3 f (a = ( A ( (a + 3 = (3 ( a = (4 (, 0 a a = (5 a = (6 = (7 = (8 (9 (0

07 6. 6.. f 0 ( f( f( f ( > 0 f ( < 0 f( f( = a = f( f( = a f(a = b f( = b f(b O a b 6.4 = 3 6 + 9 = 3 + 9 = 3( ( 3 = 0 =, 3 3 + 0 0 + = = 3 O 3

08 6.8 ( f( = 3 + 3 9 + ( ( = 3 9 + 5 ( (3 = 3 + 6 9 + ( (4 = 3 + 3 + ( (5 = 5 (3 3 9 ( 6.9 = 3 3 ( 6.0 = 3 6 9 + (JFE ( ( (3 6. f( = 3 + a + b (, 4 3 ( ( a, b ( f( (3 = f(

09 6.5 f( = 3 + a + b + c = = 3 a b c f ( = 3 + a + b f ( = 0 =, 3 ( + 3 = a 3, ( 3 = b 3 a = 3 b = 9 f( = 3 3 9 + c f(3 = 3 3 3 3 9 3 + c = c = 5 f( = ( 3 3( 9( + 5 = 0 ( a = 3 b = 9 c = 5 0 6. = 3 + a + b + c = 0 = ( ( a, b ( 6.3 = 3 + a + b + c = 3 = 3 ( 6.4 = a 3 + b + c + d = 44 = 4 64 a, b, c, d (

0 3 = a 3 +b +c+d = 0 3a +b+c = 0 D D/4 = b 3ac D/4 > 0 0 D/4 = 0 0 a D/4 < 0 a D/4 = b 3ac > 0 D/4 = b 3ac 0 3 = a 3 + b + c + d (a 0 = 3a + b + c D/4 = b 3ac D/4 D/4 = b 3ac > 0 D/4 = b 3ac = 0 D/4 = b 3ac < 0 = 0 α, β α a > 0 O α β O α O a < 0 O α β O α O 6.6 3 = 3 + 6 + a 5 a = 3 + + a = 0 D D/4 = 6 3a D > 0 a < 6.5 = 3 + a + 3 + 4 a (

6.. 6.7 = 3 ( 3 5 = 3 = 3( + ( = 0 =, 65 3 5 + 0 0 + 9 6 6 65 = 5 65 = 6 6 O 3 6 9 5 6.6 ( = 3 3 + ( 3 ( = 3 + 3 + ( 4

6.8 8cm 8cm cm (8 cm cm cm cm 3 > 0 8 > 0 0 < < 9 = (8 = 4( 3 8 + 8 = ( + 7 = ( 3( 9 0 3 9 = 3 + 0 ( 3 cm 6.7 ( 30cm ( ( 5cm 8cm ( (3 5cm 40cm cm (

3 6.9 3 6 = a a = 3 6 = 3 = 3( 4 = a = 3 6 O 4 a = a a < 3, 0 < a 0 4 + 0 0 + 0 3 3 6 = a 3 a = 0, 3 3 < a < 0 3 6.8 ( 3 6 + 9 = a 3 a ( 3 3 = a a

4 6.0 0 3 + 3 3 f( = ( 3 + 3 3 0 f ( = 3 6 + 3 f ( + 0 + = 3( f( 0 0 f( 0 f( = 0 0 0 f( 0 ( 3 + 3 3 0 3 + 3 3 = 0 6.9 ( 0 3 + 3 ( 0 3 + 6

5 6.3 6.3. f( F ( = f( f( d = F ( + C C n n = 0,, d = + C n d = n + n+ + C d = + C d = 3 3 + C F ( = f(, G ( = g( kf( d = kf ( + C k {f( + g(} d = F ( + G( + C 3 {f( g(} d = F ( G( + C 6.9 ( ( (3 5 d = 5 + C = 5 + C (6 + 3 d = 6 3 3 + 3 + C = 3 + 3 + C ( + ( d = ( + d = 3 3 + + C

6 6.30 ( d ( ( d ( (3 ( + d ( (4 (3 4 + 3 d ( (5 ( 3 d ( (6 ( 3 6 + 3 d ( (7 ( + d ( (8 ( d (

7 6.3 ( f( = 3 + ( ( f( = ( ( + ( 6. f ( = ( + (3 f( = 3 f( f( f ( = ( + (3 f( = ( + (3 d = (3 + d = 3 + + C f( = ( 3 + ( ( + C = C + C + = 3 C = f( = 3 + + 6.3 f( =, f ( = ( 3( + f( (NEC

8 6.3. F ( = f( 6.0 ( ( 4 3 b a f( d = [ ] b F ( = F (b F (a a [ ] 3 4 d = = 43 3 3 3 3 = [ ] 3 (4 3 d = 3 = ( 3 3 3 {( 3( } = 4 6.33 ( 3 3 d ( ( (3 (4 (5 (6 0 3 4 (3 d ( ( + d ( ( + 3( d ( ( + d ( ( + 4( d ( (7 3 ( + ( + d ( (8 (5 4 6 + d (NEC

9 3 b a b a b a k f( d = k b a {f( + g(}d = {f( g(}d = f( d b a b a f( d + f( d k b a b a g( d g( d 6. p q ( ( ( 3 0 3 (p + q d ( (p + q d = p ( + 3 d 3 d + q 0 3 ( + 3 d [ 3 d = p 3 = p 33 3 + q 3 = 6 3 3 p + 4q 0 ( 3 d = = 0 0 0 ] 3 ( 3 d [ + q {( + 3 ( 3 } d [ ] d = 6 0 ] 3 = 6 6 0 = 6 6.34 k ( (k + d ( 3 ( + ( + 4 d 3 ( + d

0 a a f( d = 0 a b b f( d = f( d a b a c a b c 3 f( d = f( d + f( d 3 a b c 6. 3 3 (3 + 4 d = = 0 3 0 0 (3 + 4 d 3 0 (3 + 4 d + 3 3 (3 + 4 d (3 + 4 d [ ] (3 + 4 d = 3 + 0 = ( 3 + 0 = 3 (3 + 4 d 6.35 ( 3 3 (7 9 + 5 d ( 4 ( + 3 d 4 ( + 3 d

a f(t dt f( a d f(t dt f(t dt d a a 6. f(t dt = a f( a f( = = a 0 0 = a a a =, f( = a =, 6.36 ( f( = 0 (3t t dt ( g( a a g(t dt = +

6.3.3 ( a b f( 0 = f( = a = b S = f( S = b a f( d O a S b 6.3 = + = + = = S [ ] S = ( 3 + d = 3 + ( { } 3 ( 3 S = 3 + + ( = 6 O 3 6.37 ( (NEC = 3 + 3 O 3 ( = + 4 = 4 ( (3 = + 3 = = 3 ( (4 = 3 + ( (5 = 4 (

3 ( a b f( 0 = f( = a = b S S = b a { f(}d O a = f( S S b = f( 6.3 = 4 + 3 4 + 3 = 0 =, 3 3 0 O S S = 3 { ( 4 + 3} d S 3 ] 3 = [ 3 3 + 3 = ( 33 3 + 3 3 3 ( 3 3 + 3 = 4 3 6.38 ( = ( ( = 9 + 8 ( (3 = a (a > 0 36 a (NEC

4 6.4 = 3 3 + = 3 3 + 3 3 + = 0 = 0,, 0 0 O 0 S S = 0 ( 3 3 + d + [ ] 4 [ = 4 3 + + 0 ( 4 = 4 3 + 0 + = 4 { ( 3 3 + } d 4 + 3 ( 4 4 + 3 ] ( 4 4 + 3 6.39 ( = 3 6 + 8 ( ( = ( ( ( 3 (

5 (3 a b f( g( = f( = g( = a = b S = f( S S = b a {f( g(}d O a = g( b 6.5 = 3 = 3 3 = 3 = 0, 4 S S = = = 4 0 4 0 {( 3 ( 3} d ( + 4 d [ 3 3 + ] 4 0 = 3 3 5 O 3 3 3 4 6.40 ( = = + ( ( = + 5 = ( (3 = ( = + (

6 6.4 ( 4 = = ( { 0 ( + 0 ( (3 = l + m = n (i l, m, n (ii ( (6, ( 3, 3 O (4 = 4 + 3, = 6 + (

7 6.6 = 3 + 3 + 6 (, 5 = 3 + 3 = = 5 = ( = + 3 ( 3 + 3 + 6 ( + 3 = ( ( + 3 = 3, 3 ( ( + 3 0 S S = = 3 3 {( 3 + 3 + 6 ( + 3} d ( 3 + 5 + 3 d [ 4 = 4 + 3 3 5 ] + 3 3 ( 4 = 4 + 3 3 5 { ( 3 4 + 3 4 + ( 33 3 5 } ( 3 + 3( 3 = 64 3 6.4 ( = 3 3 = 0 ( ( = 3 3 + = (NEC (3 = 3 5 + 3 (, (

8 α β ( α( β d = (β α3 6 a + b + c = 0 α β β (a + b + c d = a ( α( β d = α = β α β α ( α( β d = a (β α3 6 { (α + β + αβ} d β β d (α + β d + αβ d α α = 3 (β3 α 3 (α + β(β α + αβ(β α = 6 (β α{(β + βα + α 3(β + α + 6αβ} = 6 (β α( β + βα α = (β α3 6 α β a + b + c = 0 { ( a + b + c = a b + c } = a{ (α + β + αβ} a a = a( α( β 3 6.3 S = 3 = { ( 4 + 3} d = ( (3 3 = 4 6 3 5 6.5 S = 4 0 = 3 {( 3 ( 3} d = ( (4 0 3 = 3 6 3 ( ( 3 d 4 0 ( 4 d

(. ( 3 0 ( + 3 (3 + 6 + 6 47 (4 3 + 0 (5 p + 3p + 0 (6 6 + (7 3 5 (8 a 3a + 0 (9 + + 4 0. ( A = 3 7 + 5 ( B = 3 + 4.3 ( b4 c 7 + 3 ( (3 + (4 3a 4 d ( a.4 ( ( 3 (3 353 3 (4 4 (5 3 3b 3 8a a 4 b.5 ( ( (3 a 6 ( + ( + (4 a 3 ( ( (7 +.6 ( ( (3.7 ( (7 + 4 (8 + ( + ( ( + (.8 ( ( c ( + ( + 4 (6 (7 ( + (9 3 (4 (5 + ( (3 0 (4 + 4 a (8 (9 a b + (3 0 (4 (8 3 (5 (5 (3 + ( + ( a + (a + (a + 3 ( + ( + ( ( 3 (6 (7 ( ( + ( + 3( 4 (5 (5 (6 + ( ( + 3 + a + 3 (6 (6 +.9 ( A = B = 5 C = ( a = b = (3 A = 3 B = C =.0 a + b + c = 0 a + b = c b + c = a c + a = b (a + b(b + c(c + a + abc = ( c( a( b + abc = 0 9

. a + b + c = 0 a + b = c, b + c = a, c + a = b ( + b c + + c a ( a b + c = a b + a c + b c + b a + c a + c b + 3 = b + c a + c + a b + a + b c = a a + b b + c c + 3 = + 3 = 0 + 3. a b = c d = k a = bk c = dk ab + cd ab cd ( a + b + 3 = bk b + dk d bk b dk d = k(b + d k(b d = b + d b d a + c a c = (bk + (dk (bk (dk = k (b + d k (b d = b + d b d ab + cd ab cd = a + c a c.3 a = b = k = ak, = bk ( a = (ak a = k + a ab + b = (ak ak bk + (bk a ab + b a = + a ab + b ( pa + r qa + s pb + r qb + s pa + r qa + s = k (a ab + b a ab + b = k = pa + r ak qa + s ak = pb + r bk qb + s bk = pb + r qb + s 30 a(p + rk = a(q + sk = p + rk q + sk b(p + rk = b(q + sk = p + rk q + sk

.4 ( a + b (a + b = a a + + b b + = (a + (b 0 a + b (a + b a = 0 b = 0 a = b = ( a ab + b = a ab + b 4 + 3 4 b ( = a b + 3 4 b 0 a ab + b 0 a b = 0 b = 0 a = 0 b = 0 (3 + + z ( + z + z.5 = {( + + ( z + z + (z z + } = {( + ( z + (z } 0 + + z + z + z = 0 z = 0 z = 0 = = z ( a > 0 a > 0 a + a a + a a a = 3

( ( (a + b a + = + a b b + b a + = a b + b a + a b > 0 b a > 0 (3 a b + b a a + b b a + = 4 ( (a + b a + 4 b ( a b + c ( b d a + d = + ad c bc + bc ad + = ad bc + bc ad + ad bc > 0 bc ad > 0 ad bc + bc ad + ( a b + c d ( b a + d c ad bc bc ad + = 4 4 (. ( = 5 = 4 ( = = 3 (3 = =. ( + 7i ( 4 + 8i (3 7 + i (4 3 7i (5 7 (6 6 (7 i (8 5 (9 i (0 3 + 4i ( 0 ( 5 3 3 i (3 + i (4 8.3 5 + 5 i.4 ( 3 4 i ( i (3 3 i (4 5 3 5 i (5 5 3 i (6 i (7 i 3 (8 (9 5 (0 0 3 0 i.5 ( 0 ( 6 (3 4 + i (4 + 8 3 i.6 t = 3 ± 3i.7 ( = ± 9i 5 ( = 5 ± 7 i 6 (3 = ± 35 i 3 3

.8 ( ( (3 (4 (5 (6.9 ( k < 3 5 < k ( k < 8 < k (3 a = 6 (4 0 < k < (6 < m < 4.0 α β (5 k 5 ( α + β = αβ = 3 ( α + β = 3 αβ = 5 (3 α + β = 4 3 3 αβ =. ( (i 4 (ii (iii 4 ( (i 5 (ii (iii 9 (3 (i (ii (iii 0 3 3 9 (iv 4 (4 (5 (i 3 (ii 3 (6 (i 8 (ii 6 (7 63 (8 4. ( k = 5 ( m = 3 4 6 (3 a = 0 = 4 6 a = 35 6 3 7.3 ( p = 7 q = 0 ( a = b = 8.4 + 6 = 0.5 ( 4 + 5 = 0 ((i 4 + 0 = 0 (ii 5 7 + = 0 (3 7 + 6 + 4 = 0.6 ( 0 ( 7 (3 0 8.7 ( a = ( p = 6 (3 p = (4 p =.8 ( a = 5, b = 0 ( p = 5 q = (3 a = 5 b = 9.9 ( + ( 3 + 7 3.0 ( ( (+ ( (+ ( (3 ( ( (4 ( ( (5 ( ( 7 (6 ( + ( 3 (7 ( ( + ( 3 (8 ( + ( 6 + 4 (9 ( ( + 3( + 4 (0 ( + ( 3( ( ( + ( (3 ( ( + ( ( + ( 3. ( = ± 3 i ( = ± ±i (3 = ± ±i (4 = ± ±3 (5 = ± 4 (6 = ± 5 (7 = ± 5 ± 5. ( = ( ( = ± 3 (3 = ( (4 = 3 (5 = 3 (6 = 5 (7 = ± i (8 = 3 3.3 ( a = 3 ( = ± i.4 a = 8 b = 8 = ± 3 i 33

( 3. ( 3 ( 5 (3 0 3. ( ( 4 (3 8 (4 3.3 ( 5 ( 0 (3 0 (4 3 3.4 AB = 37 BC = 37 CA = 5 3.5 ( BC = CA ( CA 3.6 C(5, 0 ( 9 3.7 ( 6, (8, 5 (4(i 3 5 (ii (3, (iii ( 3, 4 ( C(4, 6 (3 C(, 3 AB = 5 5 3.8 ( = 3 + ( = (3 = + 3 (4 = + 5 (5 = 3 4 (6 = 3 5 3 + 3 3.9 ( = + 5 ( = 3 + 3 (3 = 4 3 + 3 (4 = 3 + 3 3 (5 = 3 3.0 ( = 5 0 ( = 3 + (3 = + 0 3. (//(6, (4//(5, ( (, ( (6 3. ( = 7 ( = 7 8 + 53 (3 = 8 4 + (4 = 4 6 4 (5 = 3 (6 = + 6 3.3 m = 3 m =, 3.4 ( = 4 3 3 ( = 6 3 + 7 3.5 B(4, 3 3.6 ( (, ( ( 3, 3.7 ( 5 7 ( 7 5 3.8 ( ( +( + = 9 ( ( +( + = 6 (3 ( +( = 5 (4 ( 3 + = 9 (5 ( 3 + ( + 4 = 5 (6 ( 3 + ( 4 = 9 3.9 ( ( +( 3 = 7 ( ( +(+ = 3 (3 ( 3 +(+ = 7 3.0 ( (4, 3 ( ( 3, 4 (3 (3, 0 (4 (, 6 (5 (, 3 (6 (, ( (7 (, 0 (8, 3. ( + ( + = 4 3. ( + 5 7 5 7 = 0 ( + + 4 8 = 0 34

3.3 ( (3, 4, (5, 0 ( 4 5 (3 4 5 5 (4 ( 5, 4 (5 (, 5 3.4 ( = 3 + 4, = 3 4 ( = (3 =, = 7 7 3.5 ( a = ±5 ( 5 < c < 5 ( 3 3.6 ( + = 5 = 5 ( = (0, 3 4 = 5 5, 4 5 3.7 (9, 0 6 > 0 < 3.8 ( < ( + < + + < 4 (3(i (4(i 0 + + 4 + 3 (ii (ii 3 > 3 4 + < 5 3.9 ( ( (3 4 3 O 3 4 O 4 O (4 (5 (6 4 4 3 O 3 O O 3 3 4 4 35

3.30 ( ( (3 4 O O O 3.3 3.3 = = 3 5 = 0 = 0 0 ( 4. ( ( (3 P P 5 O 4. 480 840 40 X 70 4.3 ( π ( π (3 88 (4 75 3 4.4 ( l = π S = 4π ( l = 4π S = 0π 3 4.5 ( ( (3 3 (4 0 (5 3 4 ( π 4.6 ( = sin O X O 660 (6 0 = sin P X π π O π π 3 π π 36

( ( = cos π π = cos 6 6 π 3 O π 6 3 π 7 6 π 5 3 π 4.7 ( = 3 sin θ = sin θ θ 3 π O π π θ ( = sin 3θ = sin θ θ 3 3 π O π θ 37

4.8 ( sin θ = 5 3 ( sin θ = 7 4, tan θ = 7 3 (3 cos θ = 4 5, tan θ = 3 4 (4 cos θ = 4 5, tan θ = 3 4 4.9 ( = 30 ( = π 6, 7 6 π (3 = 70, 50 (4 = 30 4.0 ( = 0, 30, 50, 80, 360 ( θ = π 6, 5 6 π (3 θ = 80 (4 θ = 70 (5 = 90 (6 = 0, 0, 40 (7 θ = 60, 300 4. 0 < 3 π, 4 3 π < π 4. ( = π, 7 6 π, 6 π ( 0 < π, π < < 7 6 π, 6 π < π 5 4.3 4, 5 6 + 6 6 4.4 ( ( (3 4 4 4 6 (4 4 4.5 + 3 4.6 6 6 4.7 (5 ( 6 + 4 (6 3 4 sin( + = sin cos + cos sin sin( = sin cos cos sin sin( + + sin( = sin cos ( = 75, = 5 sin 90 + sin 60 = sin 75 cos 5 sin 75 cos 5 = (sin 90 + sin 60 = + 3 4 38

4.8 ( sin(45 + α = sin 45 cos α + cos 45 sin α sin(45 α = sin 45 cos α cos 45 sin α sin(45 + α + sin(45 α = sin 45 cos α = cos α ( sin(a + B sin(a B =(sin A cos B + cos A sin B(sin A cos B cos A sin B =(sin A cos B (cos A sin B = sin A( sin B ( sin A sin B = sin A sin B 4.9 30 0 3 p 4.0 q 4. sin α cos α = + ( cos α = sin α cos α cos α = sin α cos α = tan α 4. ( 4 5 ( sin α + cos α = tan α 4.3 sin α = 5 cos α = 5 4.4 ( tan α = 4 ( tan α 3 = 3 4.5 = π 6, 5 6 π 4.6 = π 6, 5 6 π 3 = 3 π 3 4.7 ( = 30, 90 ( θ = 0 (3 θ = π 6, 3 π 4.8 39

( 5. ( (7 7 5. ( 3 ( 3 5.3 ( ( 3 5.4 a 3 5.5 ( 9 (3 65 5.6 5.5 > 8 5 4 (4 5 (5 5 5.7 ( 7 ( (3 4 (4 4 (5 5 (6 4 3 3 5.8 3 5.9 ( ( O O 5.0 ( < 3 4 < ( ( > > ( 0.5 5. ( < 3 ( 4 5. ( = 4 ( = 9 (3 = 4 (4 = (5 = 7 (6 = 3 (7 = (8 = (9 = 3 (0 = 4 6 5.3 ( = ( = 0, 3 (3 = (4 =, (5 = (6 = 3 5.4 ( (, = (3, 5, (5, 3 ( =, = 6 5.5 ( = 6 ( = 3 5.6 ( 3 ( 3 (3 0 5.7 ( 3 ( (3 3 (4 (5 4 (6 (7 5.8 3 4 5 5.9 ( 5 ( (3 3 (4 3 (5 6 (6 (7 (8 log 0 4 (9 (0 5.0 ( ( 0 (3 40

5. ( 3 ( 3 (3 3 (4 6 (5 3 4 (6 (7 4 5. ( 3 ( 3 (3 5 5.3 + a + ab + ab 5.4 ( ( z + (3 5.5 4 z 5.6 ( ( O O 3 5.7 ( 0 < < 3 ( 8 5 5.8 ( = log 3 ( =, log 5.9 ( = 03 ( = 9 (3 = 9 (4 = 5 (5 = 0 (6 = 4 (7 = 0 (8 = (9 = 0 (0 = 3 ( = ( = 35 (3 = 8 (4 = (5 =, 3 (6 = 9 + 3 ( 5 5.30 ( (, = (5, ( (, = (5,, 4, (3 (, = (7, 3 5.3 ( 0.778 (.300 (3.778 (4 3.778 (5.079 (6.8060 (7 0.778 (8 0.76 (9 0.6990 (0 0.9030 ( 0.0333 (.9363 (3 0.6990 5.3 (.994 (.994 (3 0.9647 5.33 ( (.756 5.34 ( 5 ( 9 (3 3 5.35 ( 7 ( 0 (3 34 ( 6. 4 6. ( 6 ( 4

6.3 ( 6 ( 3 (3 5 (4 (5 3 (6 5 (7 (8 7 3 7 6.4 ( 08 ( 3a 6.5 ( a =, b = ( a = 3, b = 6.6 f (a = a 6.7 5 6.8 ( = 4 3 ( = 3 +6 5 (3 f ( = 3 +8 (4 = 3 4 + 6.9 ( 4 3 + 6 + 6 + ( 6 + 6.0 ( = 0 + 3 ( = 3 (3 = 8 (4 = 6 0 + (5 f ( = 3 4 + (6 = 3 (7 = 4 3 + 3 (8 = 5 4 + 6 + (9 = 36 + 4 + 96 6. 8 + 6. f ( = 8 6.3 ( = 4 ( = 9 4 (3 = 6.4 ( = 4 4 ( = 4 4 6.5 = 6 9, = (3 34 6.6 = 7 3, = 3 6.7 ( a ( a (3 a (4 a a + 3 (5(6 3 (7(8 6 6 + (9(0 (3, (, 4 6.8 ( = 3 9 = 3 ( = 0 = (3 = 3 = 3 (4 = = 6 (5 = = 3 7 5 6.9 O 3 4

6.0 ( (0, ( = 5 = 3 (3 5 3 O 6. ( a = 3, b = 6 ( = 0 6 = (3 6 O 6. ( a = 3, b = 0 ( 6 6.3 = 3 6 + 9 6.4 a =, b = 3, c = 4, d = 6 6.5 a < 3, 3 < a 6.6 ( = 0, 3 = 8 ( = 9 = 4 33 6.7 ( 5cm 000cm 3 ( 5 cm (3 5cm 3 6.8 ( 0 < a < 4 ( a <, < a 43

6.9 ( f( = ( 3 + 3 0 f ( = 3 3 = 3( + ( f ( f( 0 0 + 0 f( 0 f( = 0 0 f( 0 ( 3 + 3 0 3 + 3 = ( f( = ( 3 + 6 0 f ( = 3 + = 3( f ( f( 0 + 0 8 + 0 f( 0 f( = 0 0 0 f( 0 ( 3 + 3 0 3 + 3 = 0 6.30 ( + C ( 4 + C (3 + + C (4 3 + 3 + C (5 4 4 + C (6 4 3 + 3 + C (7 + 4 4 + C (8 3 3 + + C 6.3 ( 3 + + C ( 3 3 + C 6.3 f( = 3 3 + 6 + 4 6 6.33 ( 0 ( 5 (3 4 (4 3 3 3 6.34 ( 3k + 3 ( 4 6.35 ( 0 ( 5 (5 39 (6 0 3 (7 54 (8 8 44

6.36 ( f ( = 3 ( g( = a = 6.37 ( 8 ( (3 3 (4 3 (5 3 3 3 3 6.38 ( 4 3 ( 9 (3 a = 6 6.39 ( 8 ( 6.40 ( 9 ( 5 (3 9 6 6.4 ( 8 ( (3 (i l =, m = 6, n = (ii 8 (4 343 3 6 3 4 9 6.4 ( 4 ( = 4 = 0 (3 4 3 45

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