fx-370ES_912ES_UsersGuide_J02

Size: px
Start display at page:

Download "fx-370ES_912ES_UsersGuide_J02"

Transcription

1 Eng Eng 3 A Eng 1 1,234 Eng a 1234= W W Eng a 123= 1W( ) S-D S-D π 72

2 A S-D π π nπ n d π c a b π c π ' f ' A S-D 1 A '5c6= f f f 73

3 2 π A 15(π)*'2c5= f 3 ' A!2e*!3= f 74

4 (CMPLX) 15 CMPLX N2 A u u 2 3 X 1, X 2, X 3 u u A i CMPLXW i i a bi i 2 3i 2+3i CMPLX A CMPLX (r θ) y( )30 CMPLX θ 16 75

5 A b a + bi r 18 (a bi ) 1 2 ('3 i) 2'3 2i i A a 2*(!3e +i)= CMPLX a 2*(!3) +i)= CMPLX 2 '2 45 = 1 i Az!2e1y( )45= CMPLX 76

6 r θ 1 2 ('3 i) = 2'3 2i = 4 30 Az 2*(!3e+i) = CMPLX 2 1 i = '2 45 Az 1+i= CMPLX θ 180 θ 180 A CMPLX 12(CMPLX) Conjg z a bi z a bi - 2 3i a CMPLX 12(CMPLX)2(Conjg) 2+3i)= 77

7 Abs, arg z a bi Z arg - 2 2i Az b = 2 a = 2 1w(Abs)2+2i= CMPLX 12(CMPLX)1(arg) 2+2i)= CMPLX A 12 CMPLX 4 'a bi - 2'2 45 = 2 2i Az 212e1y( )45 12(CMPLX)4('a bi) = CMPLX 78

8 A 12 CMPLX 3 'r θ - 2 2i = 2'2 45 Az CMPLX 2+2i12(CMPLX) 3('r θ)= (1 3i) (2i) i 2 2 a (1+3i)/ (2i)= CMPLX 79

9 () 15 N3 A 1. N3 u 2. 1(1-VAR) u u 3. u 10, 11, 12 10= 11= 12= 80

10 4. A u COMP u 6. 5 Var u Var 7. 2 o u o 81

11 8. = u A VAR X 2 A+BX 3 _+CX 2 4 ln X 5 e^x e X, Y 6 A B^X ab 7 A X^B 8 1/X 11 1 Type

12 1 8 = YesA Cancel A 11 2 Data 11 1 FREQ 18OFF ON FREQFREQ FREQ 83

13 FREQ FREQ X Y FREQ 1 COMP A = 6 84

14 X Y 0 OFF FREQ m, 1m M STO FREQ A u u u u fc de 85 ON FREQ 40 26

15 1. 2. = u Y u Edit u Edit 3. 1 Ins u 86

16 Edit u Edit 2. 2 Del-A u A A COMP 87

17 u u u u u A Type 2Data 3Edit 4Sum 5Var 6MinMax Edit Sum Var MinMax 88

18 4Sum, 5Var, 6MinMax 93 7Distr Distr 7Reg Reg e ab Reg 11()1(Type)1(1-VAR) A Sum 11()4(Sum) 1Σx 2 2 2Σx A Var 11()5(Var) 89

19 1n 2o 3xσn o = Σx n xσn = Σ (x o)2 n 4xσn 1 xσn 1= Σ (x o)2 n 1 A MinMax 11()6(MinMax) 1minX 2maxX A Distr t o xσn 11()7(Distr) 1P( 2Q( 3R( 4 't P(t), Q(t), R(t) 3 P (t) Q (t) R (t) 0 t 0 t 0 t 90

20 A 1 x 0 FREQ Nc4()1(ON)N3() 1(1-VAR) 0=1=2= 3=4=5=6= 7=9=10= cec2=c2=2 =2=3=4=2= A11()4(Sum) 1(Σx 2 )= 11()4(Sum) 2(Σx)= ()5(Var) 1(n)= 91

21 11()5(Var) 2(o)= 11()5(Var) 3(xσn)= ()6(MinMax) 1(minX)= 11()6(MinMax) 2(maxX)= 4 1 x 3 x 7 11()7(Distr) 1(P( )311() 7(Distr)4('t))= 11()7(Distr) 3(R( )711() 7(Distr)4('t))= 92

22 A 11()1(Type)2(A+BX) y = A + BX Sum 11()4(Sum) 1Σx 2 2Σx 3Σy 2 4Σy X 2 X Y 2 Y 5Σxy X Y 6Σx 3 X 3 7Σx 2 y {X 2 Y} 8Σx 4 X 4 Var 11()5(Var) 1n 2o X o = Σx n 3xσn X xσn = Σ (x o)2 n 93

23 4xσn 1 X 5p 6yσn xσn 1= Σ (x o)2 n 1 Y Σy p = n Y yσn = Σ (y p)2 n 7yσn 1 Y yσn 1= Σ (y p)2 n 1 MinMax 11()6(MinMax) 1minX 2maxX 3minY 4maxY X X Y Y Reg 11()7(Reg) 1A 2B A Σy B A =. Σx n B n B. Σxy Σx. Σy = n. Σx 2 (Σx) 2 94

24 3r 4m 5n - x r r = n. Σxy Σx. Σy {n. Σx 2 (Σx) 2 }{n. Σy 2 (Σy) 2 } x m = y A B y n = A + Bx y x 2y 3 n ym x 1Nc4()2(OFF) N3() 2(A+BX)1= 1.2=1.5= 1.6=1.9= 2.1=2.4= 2.5=2.7= 3= ce1= 95

25 1.1=1.2= 1.3=1.4= 1.5=1.6= 1.7=1.8= 2= A11()7(Reg) 1(A)= 11()7(Reg) 2(B)= 11()7(Reg) 3(r)= y 3m y311()7(reg) 4(m)= x 2n 211()7(Reg) 5(n)= A 11()1(Type)3(_+CX 2 ) y = A + BX + CX 2 Sum Var MinMax 93 96

26 Reg 11()7(Reg) 1A 2B A Σy Σx Σx A = B( ) C( 2 ) n n B n Sxy. Sx2 x 2 Sx 2 y. Sxx 2 B = Sxx. Sx 2x 2 (Sxx 2 ) 2 3C C Sx 2 y. Sxx Sxy. Sxx 2 C = Sxx. Sx2 x 2 (Sxx 2 ) 2 (Σx) Sxx 2 = Σx 2 n Sxy = Σxy (Σx. Σy) n Sxx 2 = Σx (Σx 3. Σx 2 ) n Sx 2 x 2 = Σx 4 (Σx 2 ) 2 n Sx 2 y = Σx 2 y (Σx 2. Σy) n 4m1 5m2 6n x1 m1 = B + B 2 4C(A y) 2C x2 m2 = B B 2 4C(A y) 2C y n = A + Bx + Cx 2 97

27 - 95 x 2y 3 n y m1 x1m2 x2 A11()7(Reg) 1(A)= 11()7(Reg) 2(B)= 11()7(Reg) 3(C)= y 3m1 311()7(Reg) 4(m1)= y 3m2 311()7(Reg) 5(m2)= x 2n 211()7(Reg) 6(n)= A 11()1(Type)4(ln X) y = A + BlnX 98

28 93 Σy B. Σlnx A = n n. Σ(lnx)y Σlnx. Σy B = n. Σ(lnx) 2 (Σlnx) 2 r = - {n. Σ(lnx) 2 (Σlnx) 2 }{n. Σy 2 (Σy) 2 } y A B m = e n = A + Blnx x y n. Σ(lnx)y Σlnx. Σy x 80y 73 n y m x 1Nc4()2(OFF)N3()4(In X) 29=50=74= 103=118= ce1.6= 23.5= 38=46.4= 48.9= A11()7(Reg) 1(A)= 11()7(Reg) 2(B)= 99

29 11()7(Reg) 3(r)= x 80n 8011()7(Reg) 5(n)= y 73m 7311()7(Reg) 4(m)= A e 11()1(Type)5(e^X) y = Ae BX 93 A = Σlny B exp(. Σx) n n. Σxlny B = n. Σx. Σlny Σx 2 (Σx) 2 n r. Σxlny Σx. Σlny = {n. Σx 2 (Σx) 2 }{n. Σ(lny) 2 (Σlny) 2 } lny lna m = B n = Ae Bx - x y e x 16 y 20 n ym x 100

30 1Nc4()2(OFF)N3()5(e^X) 6.9=12.9= 19.8= 26.7= 35.1= ce21.4= 15.7= 12.1=8.5= 5.2= A11()7(Reg) 1(A)= 11()7(Reg) 2(B)= 11()7(Reg) 3(r)= x 16n 1611()7(Reg) 5(n)= y 20m 2011()7(Reg) 4(m)= A ab 11()1(Type)6(A B^X) y = AB X

31 A = Σlny lnb exp(. Σx n ) n B = exp(. Σxlny Σx. Σlny ) n. Σx 2 (Σx) 2 n r. Σxlny Σx. Σlny = {n. Σx 2 (Σx) 2 }{n. Σ(lny) 2 (Σlny) 2 } lny lna m = lnb n = AB x - x 1 3 y ab x 15 y n ym x Nc4()2(OFF)N3()6(A B^X) y1=3=5= 10= ce0.24=4= 16.2=513= A11()7(Reg) 1(A)= 11()7(Reg) 2(B)= 102

32 11()7(Reg) 3(r)= x 15n 1511()7(Reg) 5(n)= y 1.02m () 7(Reg)4(m)= A 11()1(Type)7(A X^B) y = AX B 93 A = Σlny B exp(. Σlnx) n n. Σlnxlny B = n. Σlnx. Σlny Σ(lnx) 2 (Σlnx) 2 n r. Σlnxlny Σlnx. Σlny = {n. Σ(lnx) 2 (Σlnx) 2 }{n. Σ(lny) 2 (Σlny) 2 } m = e n = Ax B - x ln y ln A B y x 40 y 1000 n ym x 103

33 1Nc4()2(OFF)N3()7(A X^B) 28=30=33= 35=38= ce2410= 3033= 3895= 4491= 5717= A11()7(Reg) 1(A)= 11()7(Reg) 2(B)= 11()7(Reg) 3(r)= x 40n 4011()7(Reg) 5(n)= y 1000m () 7(Reg)4(m)= A 11()1(Type)8(1/X) y = A + X B

34 Σy B. Σx 1 A = n Sxy B = Sxx Sxy r = Sxx. Syy Sxx = Σ(x 1 ) 2 Syy = Σy 2 Sxy = Σ(x 1 )y B m = y A B n = A + x (Σy) 2 n (Σx 1 ) 2 n Σx. 1 Σy n - x y x 3.5 y 15 n ym x 1Nc4()2(OFF)N3()8(1/X) 1.1=2.1= 2.9=4= 4.9= ce18.3= 9.7=6.8= 4.9=4.1= 105

35 A11()7(Reg) 1(A)= 11()7(Reg) 2(B)= 11()7(Reg) 3(r)= x 3.5n 3.511() 7(Reg)5(n)= y 15m 1511()7(Reg) 4(m)= 106

36 n (BASE-N) BASE-N N4 n A DEC w HEX 6 BIN l OCT i U 10 Dec c 16 Hex b 2 Bin q 8 Oct BASE-N 10 BASE-N Ab1+1= 107

37 Aq7+1= 2 2 Syntax ERROR BASE-N 16 16A, B, C, D, E, F {A} {B} y e {C} w {D} s E c - 161F F t Ac1F+1= n AU30= b q 108

38 c A n BASE-N n n13(base) 2cf c 1 f A x x x x x x 7FFFFFFF x FFFFFFFF ERROR 109

39 BASE-N A n Ab13(BASE) c1(d)3 10 A Ab13(BASE) c1(d)5+ 13(BASE) c2(h)5= n 10 2 A and and (BASE) 1(and)1100= 110

40 A or or (BASE) 2(or)11010= A xor xor (BASE) 3(xor)1100= A xnor xnor (BASE) 4(xnor)101= A Not - Not (BASE) 5(Not)1010)= A Neg 2 - Neg (BASE)6(Neg) )= 111

41 (EQN) 15 EQN N5 21 X 0.5Y 3 2X 3Y 4 1. N5 EQN u EQN 2. 1 a nx b ny c n21 u 3. 1= 0.5= 3= 2= 3= 4= X 0.5Y 3 2X 3Y 4 112

42 4. = u X EQN ucf XY A 4 = X = Y Y = 1 a nx + b ny = c n 21 2 a nx + b ny + c nz = d n 31 3 ax 2 + bx + c = ax 3 + bx 2 + cx + d = A EQN N5 EQN EQN EQN 113

43 A 31 3 d COMP A = 6 A 0 A0 114

44 A A 85 = = = 1cf X, Y Z 2 3 c f X1, X2, X3 A ENG 115

45 1 X 2Y 3 2X 3Y 4 A N5(EQN) 1(a nx+b ny=c n) 1=2=3= 2=3=4= = c 2 X 2 2X 3 0 A N5(EQN) 3(aX 2 +bx+c=0) 1=2=3= 116

46 = = X Y Z 2 3 X Y Z 0 X Y Z 4 A N5(EQN) 2(a nx+b ny+c nz=d n) 1=y1=1= 2=1=1= y1=0=y1= 1=1=4= = c c 117

47 4 X 3 2X 2 X 2 0 A N5(EQN) 4(aX 3 +bx 2 +cx+d=0) 1=y2= y1=2= = c c 5 X 2 4X 4 0 A N5(EQN)3(aX 2 +bx+c=0) 1=y4=4= = 118

48 (TABLE) 15 TABLE N6 x 1 f(x) x N6 TABLE u 2. u S)(X)w+1'2 119

49 3. = u 1 u 1 4. = u 5 u 5. = u 1 u 6. = u u A 120

50 x A TABLE COMP X A, B, C, D, Y M X d/dx Pol, Rec Σ u u u u u m, 1m M u STO A x xstart End Step = x x 30 x

51 x X A x TABLEx TABLEx TABLE N6 TABLETABLE TABLE x TABLE x x f x f x A 122

52 Pol(, Rec( (, d/dx(, Σ( P(, Q(, R( sin(, cos(, tan(, sin 1 (, cos 1 (, tan 1 (, sinh(, cosh(, tanh(, sinh 1 (, cosh 1 (, tanh 1 ( log(, ln(, e^(, 10^(, '(, 3 '( arg(, Abs(, Conjg( Not(, Neg( Rnd( x 2, x 3, x 1, x!,,, r, g, ^(, x '( 't % ab /c ( ) d, h, b, o n m, n, m1, m2 npr, ncr 123

53 , π, e, 2π, 5A, πa, 2i 2' 3, Asin 30, and or, xor, xnor 2 2 x y2w= (y2)w= ( 2) /2i= 1 2i i 2 1 1/(2i)= 1 (2i) i 2 124

54 Stack ERROR A CMPLX 1 2 CMPLX 5 125

55 DEG 0 x sin x RAD 0 x GRA 0 x DEG 0 x cos x RAD 0 x GRA 0 x DEG tan x RAD sin 1 x cos 1 x GRA sin x x = (2n 1) 90 sin x x = (2n 1) π / 2 sin x x = (2n 1) x 1 tan 1 x 0 x sinh x cosh x 0 x

56 sinh 1 x 0 x cosh 1 x 1 x tanh x 0 x tanh 1 x 0 x log x / ln x 0 x x x e x x 'x 0 x x 2 x /x x ; x G 0 3 'x x x! 0 x 69 x npr 0 n , 0 r n n, r : 1 {n!/(n r)!} ncr 0 n , 0 r n n, r : 1 n!/r! n!/(n r)! Pol(x,y) Rec(r,θ ) ^(x y ) x, y x 2 +y r θ: sinx a, b, c b, c x x x 0: ylogx 100 x 0: y 0 x m 0: y n, m, n : 2n y log x

57 x 'y a b /c y 0: x G 0, /x logy 100 y 0: x 0 2n 1 y 0: x 2n 1, m G 0; m, n : m /x log y ^(x y ), x 'y, 3 ', x!, npr, ncr 1 ERROR Stack ERROR A de

58 A A de ERROR u u u u u Stack ERROR u u u

59 Syntax ERROR u u Argument ERROR u u Variable ERROR 52 u X u u X u Can t Solve 52 u u u 130

60 Insufficient MEM u TABLE u Time Out u u tol O O 19 CLR 1 Setup = Yes 131

61 fx-370es 41 fx-912es LR44 2TWO WAY POWER 132

62 u k l u u A fx-370es A(OFF) k l O19 CLR 3 All = Yes 133

63 fx-912es O A(OFF) O k O19 CLR 3 All = Yes A 6 O 134

64 fx-370es 4 : R03 UM-4 1 6,000 17, W 0 C 40 C mm 110g fx-912es G13 LR C 40 C mm 105g 135

65 ? I A B cb θ A C b B C a 10m (c) A b < b sin θ = c a cos θ = c b tan θ = a A c 60 ( θ ) B a C θ B a b > sin θ = b = c sin θ c a cos θ = a = c cos θ c az b = 10 sin 60 10s60)= C b a = 10 cos 60 10c60)= b B θa c b tanθ b sinθ a B θ b ca tanθ a cosθ 136

66 P(x,y) y 10m az 10, 60 1-(Rec)10 1)(,)60)= 0 60 x? II 2 a b B θ B c 8m (a) < B θ c a θ A b C A 5m (b) C sin θ = cos θ = tan θ = b c a c b a b b > tan θ = θ = tan a 1 a 137

67 az θ = tan t(tan 1 ) 5/8)= 60 e a a c cos 1 c b b c sin 1 c az 5m 0 θ r 8m P(8,5) 8, 5r, θ 1+(Pol)81)(,) 5)= Yθ60 tf(y)e 138

68 ? C D A X < X A sin C X = C (61 32 ) (49 25 )D sin (180 C D) > az A (50m) C, D C, D 61e32e1t(STO)w(C) 49e25e1t(STO)s(D) 50sSw(C))/s180- Sw(C)-Ss(D))=? a b c S < c (30m) b (40m) S S = s (s a)(s b)(s c) 1 a s = (a + b + c) (50m) 2 139

69 > az s A ( )/2 1t(STO)y(A) S!Sy(A)(Sy(A) -50)(Sy(A) -40)(Sy(A) -30))=? θ 20 W 60kgµ 0.3 P θ (20 ) P W (60kg) < P = W (sin θ + µ cos θ ) > az 60(s20)+ 0.3*c20)) = 140

70 ? V0 30m/s 50 θ 3h V0(30m/s) < h = V0t sin 1 θ gt 2 h 2 θ (50 ) (g: 9.8m/s 2 ) > az 30*3* s50)- 2E*9.8* 3w= 141

71 142

72 143

73 Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y 144

74 145

75 Phone SA0512-A Printed in China

fx-3650P_fx-3950P_J

fx-3650P_fx-3950P_J SA1109-E J fx-3650p fx-3950p http://edu.casio.jp RCA500002-001V04 AB2 Mode

More information

36.fx82MS_Dtype_J-c_SA0311C.p65

36.fx82MS_Dtype_J-c_SA0311C.p65 P fx-82ms fx-83ms fx-85ms fx-270ms fx-300ms fx-350ms J http://www.casio.co.jp/edu/ AB2Mode =... COMP... Deg... Norm 1... a b /c... Dot 1 2...1...2 1 2 u u u 3 5 fx-82ms... 23 fx-83ms85ms270ms300ms 350MS...

More information

26.fx95MS_Etype_J-cover_SA0311D

26.fx95MS_Etype_J-cover_SA0311D P fx-95ms fx-100ms fx-570ms fx-912ms (fx-115ms) fx-991ms English Manual Readers! Please be sure to read the important notice on the inside of the front cover of this manual. J http://www.casio.co.jp/edu/

More information

fx-JP500

fx-JP500 SA1409-A JA fx-jp500 http://edu.casio.jp RJA531983-001V01 1. 2. 1 2 15 31 + 3 ... 1... 3... 5... 5... 5... 7... 8... 9... 11... 14... 15... 17... 19... 19... 21... 26... 27... 27... 29 n... 33 /... 34...

More information

6.fx570MS-Atype_J-cover_SA0403E

6.fx570MS-Atype_J-cover_SA0403E J fx-570ms fx-991ms CA 310029-001V06 http://www.casio.co.jp/edu/ Eng n 1 fx-95ms/fx-100ms/fx-570ms/ fx-912ms (fx-115ms)/fx-991ms 2 fx-570ms/fx-991ms COMP F 1 CMPLX F 2 SD F F 1 REG

More information

fx-JP700_fx-JP900

fx-JP700_fx-JP900 SA1412-A 1. 2. 1 2 15 31 + 3 ...1...3... 5... 5... 5...7...8... 9... 11...14... 15... 17... 18... 19... 21 QR fx-jp900... 25...26... 27...27... 29 n... 32 /...34... 35... 37... 38 fx-jp900...40 fx-jp900...

More information

fx-72F

fx-72F SA1310-A JA fx-72f http://edu.casio.jp RJA528451-001V01 A!j(CLR)d(All)w 11 14 25 SD/REG 45 PRGM 73 1 ! a s!s(sin 1 )bw b(contrast) fcde REPLAY 2 1. 2. 3 u u u u 4 u u 15 5 3 1 6 ...1... 1... 1... 2...3...6...9...

More information

fx-991ES_J

fx-991ES_J J fx-991es RCA501267-001V01 http://www.casio.co.jp/edu/ A 19(CLR)3(All)=(Yes) 15 43 1 1 2 + -! A!2)+!3= 1 S sin 1 {D} s 1s(sin 1 )1= 1(Setup) fcde REPLAY 2 A a 16 z Z Deg Rad 16 3 4 u u 5 O fx-991es...

More information

fx-260A_Users Guide_J

fx-260A_Users Guide_J fx-260a http://edu.casio.jp J 1 5 2 Fl SD F0 COMP F4 DEG F5 RAD F6 GRA 3 F7 FIX F8 SCI F9 NORM COMP DEG, RAD, GRA COMP SD F0 SD SC FIX F9 SD DEG, RAD, GRA t SD COMP DEG RAD GRA COMP 23 4.5 53 23 + 4.5,

More information

I

I I 6 4 10 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............

More information

数学の基礎訓練I

数学の基礎訓練I I 9 6 13 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 3 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............

More information

e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,,

e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,, 01 10 18 ( ) 1 6 6 1 8 8 1 6 1 0 0 0 0 1 Table 1: 10 0 8 180 1 1 1. ( : 60 60 ) : 1. 1 e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1,

More information

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10

More information

(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

(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)

More information

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....

More information

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............

More information

fx-373ES_573ES_913ES_993ES_Users Guide_J

fx-373ES_573ES_913ES_993ES_Users Guide_J SA0810-A J fx-373es fx-573es fx-913es fx-993es http://edu.casio.jp RJA519978-001V01 A A 2 19(CLR)3(All)=(Yes) 10 23 1 1 2 + -! A!2)+!3= 1 S 1s(sin 1 )1= sin 1 {D} s 1(Setup) fcde REPLAY 11 11 A a z Deg

More information

( )

( ) 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...............................

More information

Note.tex 2008/09/19( )

Note.tex 2008/09/19( ) 1 20 9 19 2 1 5 1.1........................ 5 1.2............................. 8 2 9 2.1............................. 9 2.2.............................. 10 3 13 3.1.............................. 13 3.2..................................

More information

chap1.dvi

chap1.dvi 1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f

More information

fx-375ES_fx-915ES_fx-995ES_Eng

fx-375ES_fx-915ES_fx-995ES_Eng J fx-375es fx-915es fx-995es http://edu.casio.jp RJA526564-001V01 A 2 19(CLR)3(All)=(Yes) 1 1 2 + -! A!2)+!3= 1 S SHIFT 1 1s(sin 1 ) 1Y(INS) ALPHA S Sy(A) S5(e) i { } CMPLX 42 DEC HEX BIN OCT { } BASE-N

More information

untitled

untitled yoshi@image.med.osaka-u.ac.jp http://www.image.med.osaka-u.ac.jp/member/yoshi/ II Excel, Mathematica Mathematica Osaka Electro-Communication University (2007 Apr) 09849-31503-64015-30704-18799-390 http://www.image.med.osaka-u.ac.jp/member/yoshi/

More information

EL5250

EL5250 EL-5250 SHARP EL-5250 1 2 3 4 5 6 7 8 x @ "... i ;... @ F... k ;... i Q... @ ; j @ s ; A k S @ s@ ` ;; 5 NORMAL MODE 0. πrœ 10_ 9 10 y zall DATA CL?z z YES [DEL] z z NO [ENTER]z NORMAL MODE 0. @ o 0 +

More information

, 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

, 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 ,,,,.,,,. R f : R R R a R, f(a + ) f(a) lim 0 (), df dx (a) f (a), f(x) x a, f (a), f(x) x a ( ). y f(a + ) y f(x) f(a+) f(a) f(a + ) f(a) f(a) x a 0 a a + x 0 a a + x y y f(x) 0 : 0, f(a+) f(a)., f(x)

More information

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

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 ),

More information

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

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 8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,

More information

2009 I 2 II III 14, 15, α β α β l 0 l l l l γ (1) γ = αβ (2) α β n n cos 2k n n π sin 2k n π k=1 k=1 3. a 0, a 1,..., a n α a

2009 I 2 II III 14, 15, α β α β l 0 l l l l γ (1) γ = αβ (2) α β n n cos 2k n n π sin 2k n π k=1 k=1 3. a 0, a 1,..., a n α a 009 I II III 4, 5, 6 4 30. 0 α β α β l 0 l l l l γ ) γ αβ ) α β. n n cos k n n π sin k n π k k 3. a 0, a,..., a n α a 0 + a x + a x + + a n x n 0 ᾱ 4. [a, b] f y fx) y x 5. ) Arcsin 4) Arccos ) ) Arcsin

More information

高等学校学習指導要領解説 数学編

高等学校学習指導要領解説 数学編 5 10 15 20 25 30 35 5 1 1 10 1 1 2 4 16 15 18 18 18 19 19 20 19 19 20 1 20 2 22 25 3 23 4 24 5 26 28 28 30 28 28 1 28 2 30 3 31 35 4 33 5 34 36 36 36 40 36 1 36 2 39 3 41 4 42 45 45 45 46 5 1 46 2 48 3

More information

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

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,

More information

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y No1 1 (1) 2 f(x) =1+x + x 2 + + x n, g(x) = 1 (n +1)xn + nx n+1 (1 x) 2 x 6= 1 f 0 (x) =g(x) y = f(x)g(x) y 0 = f 0 (x)g(x)+f(x)g 0 (x) 3 (1) y = x2 x +1 x (2) y = 1 g(x) y0 = g0 (x) {g(x)} 2 (2) y = µ

More information

i

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,

More information

Part () () Γ Part ,

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

More information

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)

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)

More information

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

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

More information

keisoku01.dvi

keisoku01.dvi 2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 5 Mon, 2006, 401, SAGA, JAPAN Dept.

More information

c 2009 i

c 2009 i I 2009 c 2009 i 0 1 0.0................................... 1 0.1.............................. 3 0.2.............................. 5 1 7 1.1................................. 7 1.2..............................

More information

(ii) (iii) z a = z a =2 z a =6 sin z z a dz. cosh z z a dz. e z dz. (, a b > 6.) (z a)(z b) 52.. (a) dz, ( a = /6.), (b) z =6 az (c) z a =2 53. f n (z

(ii) (iii) z a = z a =2 z a =6 sin z z a dz. cosh z z a dz. e z dz. (, a b > 6.) (z a)(z b) 52.. (a) dz, ( a = /6.), (b) z =6 az (c) z a =2 53. f n (z B 4 24 7 9 ( ) :,..,,.,. 4 4. f(z): D C: D a C, 2πi C f(z) dz = f(a). z a a C, ( ). (ii), a D, a U a,r D f. f(z) = A n (z a) n, z U a,r, n= A n := 2πi C f(ζ) dζ, n =,,..., (ζ a) n+, C a D. (iii) U a,r

More information

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)

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) D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y

More information

2009 IA 5 I 22, 23, 24, 25, 26, (1) Arcsin 1 ( 2 (4) Arccos 1 ) 2 3 (2) Arcsin( 1) (3) Arccos 2 (5) Arctan 1 (6) Arctan ( 3 ) 3 2. n (1) ta

2009 IA 5 I 22, 23, 24, 25, 26, (1) Arcsin 1 ( 2 (4) Arccos 1 ) 2 3 (2) Arcsin( 1) (3) Arccos 2 (5) Arctan 1 (6) Arctan ( 3 ) 3 2. n (1) ta 009 IA 5 I, 3, 4, 5, 6, 7 6 3. () Arcsin ( (4) Arccos ) 3 () Arcsin( ) (3) Arccos (5) Arctan (6) Arctan ( 3 ) 3. n () tan x (nπ π/, nπ + π/) f n (x) f n (x) fn (x) Arctan x () sin x [nπ π/, nπ +π/] g n

More information

振動と波動

振動と波動 Report JS0.5 J Simplicity February 4, 2012 1 J Simplicity HOME http://www.jsimplicity.com/ Preface 2 Report 2 Contents I 5 1 6 1.1..................................... 6 1.2 1 1:................ 7 1.3

More information

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

(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) 2017 12 9 4 1 30 4 10 3 1 30 3 30 2 1 30 2 50 1 1 30 2 10 (1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) (1) i 23 c 23 0 1 2 3 4 5 6 7 8 9 a b d e f g h i (2) 23 23 (3) 23 ( 23 ) 23 x 1 x 2 23 x

More information

*3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i i r 3r + 4i 1 i 1 i *4 1 i 9 i 1 1 i i 3 9 +

*3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i i r 3r + 4i 1 i 1 i *4 1 i 9 i 1 1 i i 3 9 + 1 2 IT 1 *1 1 2 3 π i 1i 2i 3i πi i 2 1 *2 2 + 3 + 4i π ei 3 4 4 2 2 *1 *2 x 2 + 1 = x 2 + x + 1 = 2 3 1 2 2 2 2 *3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i 1 2 1 2 2 1 i r 3r + 4i 1

More information

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 =

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 = #A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/

More information

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

More information

D xy D (x, y) z = f(x, y) f D (2 ) (x, y, z) f R z = 1 x 2 y 2 {(x, y); x 2 +y 2 1} x 2 +y 2 +z 2 = 1 1 z (x, y) R 2 z = x 2 y

D xy D (x, y) z = f(x, y) f D (2 ) (x, y, z) f R z = 1 x 2 y 2 {(x, y); x 2 +y 2 1} x 2 +y 2 +z 2 = 1 1 z (x, y) R 2 z = x 2 y 5 5. 2 D xy D (x, y z = f(x, y f D (2 (x, y, z f R 2 5.. z = x 2 y 2 {(x, y; x 2 +y 2 } x 2 +y 2 +z 2 = z 5.2. (x, y R 2 z = x 2 y + 3 (2,,, (, 3,, 3 (,, 5.3 (. (3 ( (a, b, c A : (x, y, z P : (x, y, x

More information

熊本県数学問題正解

熊本県数学問題正解 00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (

More information

211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,

More information

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 (

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 ( 1 1.1 (1) (1 + x) + (1 + y) = 0 () x + y = 0 (3) xy = x (4) x(y + 3) + y(y + 3) = 0 (5) (a + y ) = x ax a (6) x y 1 + y x 1 = 0 (7) cos x + sin x cos y = 0 (8) = tan y tan x (9) = (y 1) tan x (10) (1 +

More information

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59

More information

solutionJIS.dvi

solutionJIS.dvi May 0, 006 6 morimune@econ.kyoto-u.ac.jp /9/005 (7 0/5/006 1 1.1 (a) (b) (c) c + c + + c = nc (x 1 x)+(x x)+ +(x n x) =(x 1 + x + + x n ) nx = nx nx =0 c(x 1 x)+c(x x)+ + c(x n x) =c (x i x) =0 y i (x

More information

(1) θ a = 5(cm) θ c = 4(cm) b = 3(cm) (2) ABC A A BC AD 10cm BC B D C 99 (1) A B 10m O AOB 37 sin 37 = cos 37 = tan 37

(1) θ a = 5(cm) θ c = 4(cm) b = 3(cm) (2) ABC A A BC AD 10cm BC B D C 99 (1) A B 10m O AOB 37 sin 37 = cos 37 = tan 37 4. 98 () θ a = 5(cm) θ c = 4(cm) b = (cm) () D 0cm 0 60 D 99 () 0m O O 7 sin 7 = 0.60 cos 7 = 0.799 tan 7 = 0.754 () xkm km R km 00 () θ cos θ = sin θ = () θ sin θ = 4 tan θ = () 0 < x < 90 tan x = 4 sin

More information

1 3 1.1.......................... 3 1............................... 3 1.3....................... 5 1.4.......................... 6 1.5........................ 7 8.1......................... 8..............................

More information

arctan 1 arctan arctan arctan π = = ( ) π = 4 = π = π = π = =

arctan 1 arctan arctan arctan π = = ( ) π = 4 = π = π = π = = arctan arctan arctan arctan 2 2000 π = 3 + 8 = 3.25 ( ) 2 8 650 π = 4 = 3.6049 9 550 π = 3 3 30 π = 3.622 264 π = 3.459 3 + 0 7 = 3.4085 < π < 3 + 7 = 3.4286 380 π = 3 + 77 250 = 3.46 5 3.45926 < π < 3.45927

More information

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ 1 (1) ( i ) 60 (ii) 75 (iii) 15 () ( i ) (ii) 4 (iii) 7 1 ( () r, AOB = θ 0 < θ < ) OAB A OB P ( AB ) < ( AP ) (4) 0 < θ < sin θ < θ < tan θ 0 x, 0 y (1) sin x = sin y (x, y) () cos x cos y (x, y) 1 c

More information

1 n A a 11 a 1n A =.. a m1 a mn Ax = λx (1) x n λ (eigenvalue problem) x = 0 ( x 0 ) λ A ( ) λ Ax = λx x Ax = λx y T A = λy T x Ax = λx cx ( 1) 1.1 Th

1 n A a 11 a 1n A =.. a m1 a mn Ax = λx (1) x n λ (eigenvalue problem) x = 0 ( x 0 ) λ A ( ) λ Ax = λx x Ax = λx y T A = λy T x Ax = λx cx ( 1) 1.1 Th 1 n A a 11 a 1n A = a m1 a mn Ax = λx (1) x n λ (eigenvalue problem) x = ( x ) λ A ( ) λ Ax = λx x Ax = λx y T A = λy T x Ax = λx cx ( 1) 11 Th9-1 Ax = λx λe n A = λ a 11 a 12 a 1n a 21 λ a 22 a n1 a n2

More information

f(x) = x (1) f (1) (2) f (2) f(x) x = a y y = f(x) f (a) y = f(x) A(a, f(a)) f(a + h) f(x) = A f(a) A x (3, 3) O a a + h x 1 f(x) x = a

f(x) = x (1) f (1) (2) f (2) f(x) x = a y y = f(x) f (a) y = f(x) A(a, f(a)) f(a + h) f(x) = A f(a) A x (3, 3) O a a + h x 1 f(x) x = a 3 3.1 3.1.1 A f(a + h) f(a) f(x) lim f(x) x = a h 0 h f(x) x = a f 0 (a) f 0 (a) = lim h!0 f(a + h) f(a) h = lim x!a f(x) f(a) x a a + h = x h = x a h 0 x a 3.1 f(x) = x x = 3 f 0 (3) f (3) = lim h 0 (

More information

30 (11/04 )

30 (11/04 ) 30 (11/04 ) i, 1,, II I?,,,,,,,,, ( ),,, ϵ δ,,,,, (, ),,,,,, 5 : (1) ( ) () (,, ) (3) ( ) (4) (5) ( ) (1),, (),,, () (3), (),, (4), (1), (3), ( ), (5),,,,,,,, ii,,,,,,,, Richard P. Feynman, The best teaching

More information

4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X

4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X 4 4. 4.. 5 5 0 A P P P X X X X +45 45 0 45 60 70 X 60 X 0 P P 4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P 0 0 + 60 = 90, 0 + 60 = 750 0 + 60 ( ) = 0 90 750 0 90 0

More information

II 2 II

II 2 II II 2 II 2005 yugami@cc.utsunomiya-u.ac.jp 2005 4 1 1 2 5 2.1.................................... 5 2.2................................. 6 2.3............................. 6 2.4.................................

More information

I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )

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

More information

( ) 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) (

( ) 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) ( 6 20 ( ) sin, cos, tan sin, cos, tan, arcsin, arccos, arctan. π 2 sin π 2, 0 cos π, π 2 < tan < π 2 () ( 2 2 lim 2 ( 2 ) ) 2 = 3 sin (2) lim 5 0 = 2 2 0 0 2 2 3 3 4 5 5 2 5 6 3 5 7 4 5 8 4 9 3 4 a 3 b

More information

() 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)

() 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) 0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()

More information

29

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

More information

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f 22 A 3,4 No.3 () (2) (3) (4), (5) (6) (7) (8) () n x = (x,, x n ), = (,, n ), x = ( (x i i ) 2 ) /2 f(x) R n f(x) = f() + i α i (x ) i + o( x ) α,, α n g(x) = o( x )) lim x g(x) x = y = f() + i α i(x )

More information

(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

(1.2) 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

More information

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63> 常微分方程式の局所漸近解析 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. http://www.morikita.co.jp/books/mid/007651 このサンプルページの内容は, 初版 1 刷発行当時のものです. i Leibniz ydy = y 2 /2 1675 11 11 [6] 100 Bernoulli Riccati 19 Fuchs

More information

Microsoft Word - 触ってみよう、Maximaに2.doc

Microsoft Word - 触ってみよう、Maximaに2.doc i i e! ( x +1) 2 3 ( 2x + 3)! ( x + 1) 3 ( a + b) 5 2 2 2 2! 3! 5! 7 2 x! 3x! 1 = 0 ",! " >!!! # 2x + 4y = 30 "! x + y = 12 sin x lim x!0 x x n! # $ & 1 lim 1 + ('% " n 1 1 lim lim x!+0 x x"!0 x log x

More information

( z = x 3 y + y ( z = cos(x y ( 8 ( s8.7 y = xe x ( 8 ( s83.8 ( ( + xdx ( cos 3 xdx t = sin x ( 8 ( s84 ( 8 ( s85. C : y = x + 4, l : y = x + a,

( z = x 3 y + y ( z = cos(x y ( 8 ( s8.7 y = xe x ( 8 ( s83.8 ( ( + xdx ( cos 3 xdx t = sin x ( 8 ( s84 ( 8 ( s85. C : y = x + 4, l : y = x + a, [ ] 8 IC. y d y dx = ( dy dx ( p = dy p y dx ( ( ( 8 ( s8. 3 A A = ( A ( A (3 A P A P AP.3 π y(x = { ( 8 ( s8 x ( π < x x ( < x π y(x π π O π x ( 8 ( s83.4 f (x, y, z grad(f ( ( ( f f f grad(f = i + j

More information

n ( (

n ( ( 1 2 27 6 1 1 m-mat@mathscihiroshima-uacjp 2 http://wwwmathscihiroshima-uacjp/~m-mat/teach/teachhtml 2 1 3 11 3 111 3 112 4 113 n 4 114 5 115 5 12 7 121 7 122 9 123 11 124 11 125 12 126 2 2 13 127 15 128

More information

IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................

More information

70 : 20 : A B (20 ) (30 ) 50 1

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...............................................

More information

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63> 電気電子数学入門 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. http://www.morikita.co.jp/books/mid/073471 このサンプルページの内容は, 初版 1 刷発行当時のものです. i 14 (tool) [ ] IT ( ) PC (EXCEL) HP() 1 1 4 15 3 010 9 ii 1... 1 1.1 1 1.

More information

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

1.2 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

More information

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s [ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =

More information

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4 1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev

More information

. sinh x sinh x) = e x e x = ex e x = sinh x 3) y = cosh x, y = sinh x y = e x, y = e x 6 sinhx) coshx) 4 y-axis x-axis : y = cosh x, y = s

. sinh x sinh x) = e x e x = ex e x = sinh x 3) y = cosh x, y = sinh x y = e x, y = e x 6 sinhx) coshx) 4 y-axis x-axis : y = cosh x, y = s . 00 3 9 [] sinh x = ex e x, cosh x = ex + e x ) sinh cosh 4 hyperbolic) hyperbola) = 3 cosh x cosh x) = e x + e x = cosh x ) . sinh x sinh x) = e x e x = ex e x = sinh x 3) y = cosh x, y = sinh x y =

More information

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

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,

More information

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

A(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6 1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67

More information

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 =

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 =

More information

85 4

85 4 85 4 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t 4.1.1 t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V

More information

( ) : 1997

( ) : 1997 ( ) 2008 2 17 : 1997 CMOS FET AD-DA All Rights Reserved (c) Yoichi OKABE 2000-present. [ HTML ] [ PDF ] [ ] [ Web ] [ ] [ HTML ] [ PDF ] 1 1 4 1.1..................................... 4 1.2..................................

More information

Excel ではじめる数値解析 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.

Excel ではじめる数値解析 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. Excel ではじめる数値解析 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. http://www.morikita.co.jp/books/mid/009631 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. Excel URL http://www.morikita.co.jp/books/mid/009631 i Microsoft Windows

More information

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H 199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)

More information

20 6 4 1 4 1.1 1.................................... 4 1.1.1.................................... 4 1.1.2 1................................ 5 1.2................................... 7 1.2.1....................................

More information

関数電卓 マニュアル

関数電卓 マニュアル 関数電卓 マニュアル EXE もくじ p EXE 電源の On/Off p3 EXE EXE S D 変換 p4 EXE リプレイ機能 p5 EXE 計算履歴 p6 EXE FUNCTION EXIT p7 EXE 微分 積分 p8 p9 EXE の計算 p0 EXE log の底の設定 p EXE 乗数 p EXE ソルブ機能 p3 EXE カルク機能 p4 EXE 内蔵公式 p5 EXE テーブルモード

More information

2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t) = x 0 + v 0 t 1 2 gt2 v(t) = v 0 gt t x = x 0 + v2 0 2g v2 2g 1.1 (x, v) θ

2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t) = x 0 + v 0 t 1 2 gt2 v(t) = v 0 gt t x = x 0 + v2 0 2g v2 2g 1.1 (x, v) θ 1 1 1.1 (Isaac Newton, 1642 1727) 1. : 2. ( ) F = ma 3. ; F a 2 t x(t) v(t) = x (t) v (t) = x (t) F 3 3 3 3 3 3 6 1 2 6 12 1 3 1 2 m 2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t)

More information

さくらの個別指導 ( さくら教育研究所 ) A a 1 a 2 a 3 a n {a n } a 1 a n n n 1 n n 0 a n = 1 n 1 n n O n {a n } n a n α {a n } α {a

さくらの個別指導 ( さくら教育研究所 ) A a 1 a 2 a 3 a n {a n } a 1 a n n n 1 n n 0 a n = 1 n 1 n n O n {a n } n a n α {a n } α {a ... A a a a 3 a n {a n } a a n n 3 n n n 0 a n = n n n O 3 4 5 6 n {a n } n a n α {a n } α {a n } α α {a n } a n n a n α a n = α n n 0 n = 0 3 4. ()..0.00 + (0.) n () 0. 0.0 0.00 ( 0.) n 0 0 c c c c c

More information

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1 I, A 25 8 24 1 1.1 ( 3 ) 3 9 10 3 9 : (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4), (3,3,3) 10 : (1,3,6), (1,4,5), (2,2,6), (2,3,5), (2,4,4), (3,3,4) 6 3 9 10 3 9 : 6 3 + 3 2 + 1 = 25 25 10 : 6 3 + 3 3

More information

II (No.2) 2 4,.. (1) (cm) (2) (cm) , (

II (No.2) 2 4,.. (1) (cm) (2) (cm) , ( II (No.1) 1 x 1, x 2,..., x µ = 1 V = 1 k=1 x k (x k µ) 2 k=1 σ = V. V = σ 2 = 1 x 2 k µ 2 k=1 1 µ, V σ. (1) 4, 7, 3, 1, 9, 6 (2) 14, 17, 13, 11, 19, 16 (3) 12, 21, 9, 3, 27, 18 (4) 27.2, 29.3, 29.1, 26.0,

More information

di-problem.dvi

di-problem.dvi 005/05/05 by. I : : : : : : : : : : : : : : : : : : : : : : : : :. II : : : : : : : : : : : : : : : : : : : : : : : : : 3 3. III : : : : : : : : : : : : : : : : : : : : : : : : 4 4. : : : : : : : : : :

More information

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =

More information

http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................

More information

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t 1 1 2 2 2r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t) V (x, t) I(x, t) V in x t 3 4 1 L R 2 C G L 0 R 0

More information

1 [ 1] (1) MKS? (2) MKS? [ 2] (1) (42.195k) k 2 (2) (3) k/hr [ 3] t = 0 10 ( 1 velocity [/s] 8 4 O

1 [ 1] (1) MKS? (2) MKS? [ 2] (1) (42.195k) k 2 (2) (3) k/hr [ 3] t = 0 10 ( 1 velocity [/s] 8 4 O : 2014 4 10 1 2 2 3 2.1...................................... 3 2.2....................................... 4 2.3....................................... 4 2.4................................ 5 2.5 Free-Body

More information

DVIOUT

DVIOUT A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)

More information

function2.pdf

function2.pdf 2... 1 2009, http://c-faculty.chuo-u.ac.jp/ nishioka/ 2 11 38 : 5) i) [], : 84 85 86 87 88 89 1000 ) 13 22 33 56 92 147 140 120 100 80 60 40 20 1 2 3 4 5 7.1 7 7.1 1. *1 e = 2.7182 ) fx) e x, x R : 7.1)

More information

a, b a bc c b a a b a a a a p > p p p 2, 3, 5, 7,, 3, 7, 9, 23, 29, 3, a > p a p [ ] a bp, b p p cq, c, q, < q < p a bp bcq q a <

a, b a bc c b a a b a a a a p > p p p 2, 3, 5, 7,, 3, 7, 9, 23, 29, 3, a > p a p [ ] a bp, b p p cq, c, q, < q < p a bp bcq q a < 22 9 8 5 22 9 29 0 2 2 5 2.............................. 5 2.2.................................. 6 2.3.............................. 8 3 8 4 9 4............................. 9 4.2 S(, a)..............................

More information

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1.

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1. 1.1 1. 1.3.1..3.4 3.1 3. 3.3 4.1 4. 4.3 5.1 5. 5.3 6.1 6. 6.3 7.1 7. 7.3 1 1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N

More information

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 +

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 + 6 ( ) 6 5 ( ) 4 I II III A B C ( ) ( ), 5 7 I II III A B C ( ) () x π y π sin x sin y =, cos x + cos y = () b c + b + c = + b + = b c c () 4 5 6 n ( ) ( ) ( ) n ( ) n m n + m = 555 n OAB P k m n k PO +

More information