DVIOUT-講

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2 1 [1] [] [3] [4] (a + b) = a +ab + b [5] (a + b) 3 a 3 +a b + ab + a b +ab + b 3 a 3 +3a b +3ab + b 3 [6] (a + b) 4 (a + b) 5 [7] technology expand((a+b) n n =?) [8] technology n =6, 7, 8, 9, (a + b) 100 a,b a p b n p a a 99 b+ +100ab 99 + b 100 3

3 n = n (a + b) 100 technology =50 99 = 4950, = (a + b) n n(n 1) n(n 1)(n ) n(n 1)(n )(n 3) 1, n,,, 6 4, 3

4 1, 1, 1 3, (a + b) n a n +na n 1 n(n 1) b+ a n b + 1 n(n 1)(n ) 1 3 a n 3 b 3 + n(n 1)(n )(n 3) a n 4 b ! 0! technology ! 100 nd W enter 4

5 a + b = c technology 3 +4 =5,5 +1 =13,8 +6 =10,7 +4 =5,1 +16 =0,40 +9 =41, =53,0 +1 =9, technology ( ) +(134567) = ( ) (n n) +(n 1) =(n n +1) 11 [3] 3 [1] [] 1 3,4,5 5

6 3 (a + b) n [1] [] 4 6

7 [3] 8 [4] [1] [] [3] x 7

8 =,1 + 1 =,0 + 1 = 1,0 + =,1+=3=0,3+=4= m +1, 3n + m, n (3m +1)+(3n +)= 3m +3n +3=3(m + n +1). m + n +1 3(m + n +1) (a + b) n [1] 5 8

9 [] [3] 1 5 [4] 6 [5] (a + b) n ( 4 0 4a 4 1 4a a a +3 a =4a +(4a +1)=8a +1 8a 1 =4a +(4a +)=8a + 8a =(4a +1)+(4a +3)=8a +4=4(a +1).a 0 9

10 =(4a +)+(4a +3)=8a +5=4(a + 1) + 1.4(a +1) n n 1 1: 10

11 abcdefg 7 a b c d e f 10 + g = (99999a b c + 994d +98e +7f)+8a +5b +4c +6d +e +3f + g =7( a + b + c + d + e + f)+8a +5b +4c +6d +e +3f + g 7 8a +5b +4c +6d +e +3f + g 8a +5b +4c +6d +e +3f + g =7(a + b + c + d)+a +e +3f + g b 3c d 7 a b 3c d +e +3f + g 1,, 3, 1,, 3, 1 9 pqrstuvwx 7 p q r s t u v w 10 + x = 7( p q r s + 148t + 14u +14v + w) +p +3q + r +5s +4t +6u +v +3w + x 7 p +3q + r +5s +4t +6u +v +3w + x p+3q+r+5s+4t+6u+v+3w+x =p+3q+r+7(s+t+u) s 3t u+v+3w+x 7 p +3q + r s 3t u +v +3w + x, 3, 1,, 3, 1,, 3, 1 1, 3,, 1, 3, a + b 10 + c d e a +3b +c d 3e f + g +3h +i ( ) n technology 11

12 5 x n 1 n =, 3, 4, 5, 6, x 1=(x 1)(x +1) 1 x 3 1=(x 1)(x + x +1) x 4 1=(x 1)(x +1)(x +1) 3 x 5 1=(x 1)(x 4 + x 3 + x + x +1) 4 x 6 1=(x 1)(x +1)(x + x +1)(x x +1) 5 x 7 1=(x 1)(x 6 + x 5 + x 4 + x 3 + x + x +1) 6 x 8 1=(x 1)(x +1)(x +1)(x 4 +1) 7 x 9 1=(x 1)(x + x +1)(x 6 + x 3 +1) 8 x 10 1=(x 1)(x +1)(x 4 + x 3 + x + x +1)(x 4 x 3 + x x +1) 9 x 11 1=(x 1)(x 10 + x 9 + x 8 + x 7 + x 6 + x 5 + x 4 + x 3 + x + x +1) 10 x 1 1=(x 1)(x +1)(x +1)(x + x +1)(x x +1)(x 4 x +1) 11 x 13 1=(x 1)(x 1 + x 11 + x 10 + x 9 + x 8 + x 7 + x 6 + x 5 + x 4 + x 3 + x + x +1) 1 - [1] n [] (x 1) [3] n (x 1) x n 1 n,n 3 1 [4] n (x 1) [5] n (x 1)(x +1) [6] n 3 (x 1)(x + x +1) [7] n (x 1)(x n 1 + x n + + x + x +1) [8] n 4 (x 1)(x +1)(x +1) [9] n 5 (x 1)(x 4 + x 3 + x + x +1) 1

13 [10] n 6 (x x +1) Xn 1 [11] x n 1=(x 1)( x k ) k=0 [1] x 3n 1=(x 1)(x + x +1) (x a + x b +1 c ) x 3n+1 1=(x 1)(x + x +1) (x a + x b +1 c )(x 3a + x 3b +1 3c ) [13],+,,+ [14] x 4n+ 1 [15] x n 1=(x 1)(x +1)(x +1)(x 4 +1) (x n 1 +1) [16] x [17] x n 1 (x 1) (x n 1 + x n + +x +x+1) x n 1=(x 1)(x n 1 +x n + +x +x+1) [18] x n 1=(x 1)(x n 1 + x n + + x + x +1) = x n + x n 1 + x n + + x + x x n 1 x n x x 1 = x n 1= [19] x n 1=(x n 1)(x n +1) [0] x 3n 1=(x n 1)(x n + x n +1) [1] n [] n (x 1) [3] x 6 3n 1 1=(x 1)(x+1)(x +x+1)(x x+1) (x 6 3n +x 3 3n +1)(x 6 3n x 3 3n +1) [4] p x p 1=(x 1)(x+1) (x p 1 +x p + +1)(x p 1 x p + +1) [5] n m x n 1 x m 1 [6] x n 1 n 13

14 [7] x n 1 n n [8] x n 1 n = 3 n (x 1) 3 n = n [9] x 1 [30] n (x 1)(x +1) [31] n = p m (p (a) (x 1) m (b) (x 1) p (c) (x 1) p [3] n 14

15 6 tan θ = t tan θ = 3 tan θ = t technology tan 1 f 1 III tan 1 t, R 1+t dx technology tan 1 t y = 1 x y θ A C B(t, 1 t ) G O D E F x y = 1 x

16 B f 0 (x) =x y = tx 1 t BC y = 1 t x + 1 t +1 F ( 1 t3 +1, 0) BCD = FBE = α tan α = t α =tan 1 t β = θ + AB α = 3π AB = R t 0 1+x dx OB + BC + CA =(t, 1 t ) ³cos( 3π + α), sin( 3π α + +(cosβ, sin β) R t 0 1+x dx tan 1 t x = t cos( 3π +tan 1 t)+cos( 3π log 1+t + t y = 1 t sin( 3π +tan 1 t)+sin( 3π log 1+t + t t t +1 t t +1 +tan 1 t) +tan 1 t) 16

17 7 OP + PA = r + p (r cos θ 1) + r sin θ = r = 3 4 cosθ r = c a, b, c, θ a b cos θ r θ P(r cos θ,rsin θ) A(1, 0) [1] c c a, b c [] a b (a) (b) (c) a = b a > b a < b [3] θ (a) θ θ + π π (b) θ nθ(n r = (n =1) 10 +cosnθ (n =) (n =3) (n =4) (n =5) n 17

18 1 3 ( 1 :r = 10 +cosθ :r = 10 +cosθ 3 r = 10 +cosθ θ 5 π +cosθ window 30 <x<30, 30 <y<30,xscl yscl 0.1 [1] r = [] r = [3] r = 10 +cosθ cos3θ 10 +cosθ cos4θ 10 +cosθ 10 +cosθ 18

19 8 [1] 1 B [] [3] [4] (function ) [5] function9 r Ãr 100 x x y1 = x 100 x 7 9 x 9! +10 y = 100 x µ r 3.1 y3 = 4x x x 3.1 x r x y4 =7.6 y5 = x r 9 x 9 x (x.93368)(x 1.5)x(x +1.5)(x ) +7.6 r 100 x y6 == 100 x x v ³ x ( ) 7 y7 = u t ³ x ( ) 7 y8 = p 5 (x + 30) +8 y9 = p 5 (x +30) +8 [6] style line [7] Axes=off [8] graph order SQE [9] Window x +1 (x 17) xmin=-39, xmax=39,xscl=, ymin=-1, ymax=37, yscl=,xres=1 19

20 [10] 0

21 [1] 1 A [] [3] sunset [4] ( ) [5] parametric ( xt1 = 3cost +4π xt50(t) yt1 =3sint xt4 = yt4 = xt3 = xt = 5t π yt50(t) yt =4.5 1t 1 [t] 6 +4π [t] xt51(t) yt3 = t sin µ(t ) cos(t ) t xt7 = yt7 = xt5 = tan(t ) + cos(t ) + rand() yt51(t) t +5π xt5(t)+yt5(t) yt5 = sin(t) +8 t 4 ½ xt6 =.5t yt6 =rand() 4 t π +6π + xt53(t) ³ sin( t rand() )+ 3 µ t π 0. t π 0. xt8 = 4t yt8 = 3 µ t 9 8 t t 4 xt9 = yt53(t) +.5 yt9 = 3t

22 xt53 = ( xt10 = rand() 4 yt10 = rand() xt11 = t µ xt54(t) yt11 = ( 1) [ t 3. ] xt50 = yt50 = xt51 = yt51 = xt5 = yt5 = t +0.1 t+0.1 t t t π t π t t 4.7 t t 9.5 t t t t t π +0.4 t π 0.5 t π+0.4 t π 0.5 t π +0.4 t π 0.5 t π+0.4 t π 0.5 t 4π 0.1 t 4π 0.1 yt53 = 1 t t 1.5 t.5 + t.7 t 4.1 t 1.3 t 1.5 t.5 t.7 t 4.1 ( xt54 = t 6.5 t xt50 yt50 check [6] style xt6,yt6,xt10,yt10 dot line [7] angle radian [8] graph order simul [9] Window tmin=0,tmax=1,tstep=0.,xmin=0, xmax= xscl=5, ymin=0, ymax=10, yscl=1

23 [10] g(x) = 1 µ x x x 3 0 <x<3 x 3 on 3

24 9 [1] [] [3] [4] (1) () (3) (4) (5) (6) (7) (8) (9) [5] (1) [6] () [7] (5) x + x [8] (4) x x [9] (3) [10] (6) [11] x x table 0 [1] 1 x x [13] (7) 4

25 [14] x x (7) F6 style [15] (7), [16] 1 x + x [17] (6) x + x x + x [18] (9) x x + x x [19] (8) x x x x [0] (8)(9) [1] [] (9) [x] int(x) [3] [x] table [4] [5] 1Km 10 1km 0 1Km 10 [6] 10 [x] 10 [x] [0.1x] 10 [x] 1km 10 [0.1x] trace [7] 10 [x]

26 [8] [ x]. x y [ x +1] [9] 5Km 0 1km y = 5[ x +5] +5[x] ( table [10] 5[x] 5[ x +5] [11] 5Km 0 3Km 50 Km 100 (

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

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210 資料 TI 89 (1) TI 89 2nd ON HOME ( ) ( ) HOME =! ENTER ( ) = (10) ENTER ( ) [ ] { } ( )! 2 =! ( ) ( ) 2 3x ( 2y + yz) ( ) 3x ( ( ) 2y + y z) 210 資料 TI 89 (1) TI 89 2nd ON HOME () () HOME =! ENTER () = 3 10 3 (10) ENTER ( ) [ ] { } ( )! 2 =! ( ) () 2 3x ( 2y + yz) ( ) 3x ( ( ) 2y + y z) ENTER () 2nd 9 2nd 9) ENTER ( ) 2nd 7) ENTER 7 7 ) ENTER

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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 4 4 5 4 I II III A B C, 5 7 I II A B,, 8, 9 I II A B O A,, Bb, b, Cc, c, c b c b b c c c OA BC P BC OP BC P AP BC n f n x xn e x! e n! n f n x f n x f n x f k x k 4 e > f n x dx k k! fx sin x cos x tan

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29

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