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曲陆
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1 (III)

2 4.

3 T,T T d l d T Q Q ~ T~, d~, k~ T d T Q k d T Q

4 Q Q T a ~ T b ~ k ~ k ~ k T d T k T l T T k T d T a d l T T b a a b b T T k Q k, s h h d s + ) k, ( l d d T Q

5 Q d T T k Q d T T Q ) ( + s d T T k Q d l h k k h s s Q Q +,, Q Q < k ~8 0-3, k.5 0-4, k /k 6 ~3 Q Q d l h h Q Q +, 8 k /k 6

6 Q Q h 8h +, hl/d4, Q /Q 0.03 l d Q /Q 97% Q /Q k h

7 Discussions

8 5.

10 0000

11 v n m mkn w r t0 n0. tn vkw r

12 tn. i r+wi, m tvt, m i π ( r t + wi) vt m π wk π rk n + v v kn n

13 . 3. tt+dt π [( r + wkn ) r ] wvt ( r + wkn )πkdn vdt t π wk π rk n + v v n

14 m i π ( r + wi ) π [( r + wkn ) r ] ( r + wkn )πkdn vt wvt vdt t π wk π rk n + v v n r, w, v, k,

15 t an + bn, a,b t84, n606, (t, n) t n a.6 0, t n b.45 0.

16 t an + bn ( a.6 0, b ) n 4450 t t n a,b

17 Discussions

18 6.

19 AB θ α α θ A B

20 ()w p w ww +w w f +f p p p f ~ α w p pp +p f f w w p ~ θ ws p s s s

21 w f, p vff -p wks, pks v w wsin(θ-α) α f w sinαwsinα sin(θ-α) f f w p pcosθ w vk θ (f -p ) v v vcosθ p p p w

22 v vcosθ k (f -p )cosθ f w sinαwsinα sin(θ-α) p pcosθ θ,α, v ) θαf f w[cos(θ-α)-cosθ]/ α θ / f w(-cosθ)/ ) α θ /, v k [w(-cosθ)/ -pcosθ]cos θ θv wks, pks θ f f p v α w w v p p w

23 v k [w(-cosθ)/ -pcosθ]cos θ ( k w/)[-(+p/w)cosθ]cos θ v k( t s >> s wks, pks t+s /s, k k w/ cosθ ) cosθ < t < k t[ (cos θ 4t s cosθ ( t + ), α t s θ /4<cos θ</ t ) v 60 º < θ < 75 º ] B

24 Discussions

25 7.

27 ()

28 y y 0 0 yf(x)~x xg(y)~y x0 yy 0 y 0 ~ y 0 ~ y y 0 + x y yf(x) y y f ( x < y + x 0 < ) 0 x yf(x) P(x y m,y m ) xg(y) y 0 0 x x 0 x P~()

29 x<y xy y<x<y s ~ x y x, sxy x y 0 sx+y x y 0 sy yy 0 /s y y 0 +(-s)x x ys (x y) y (x y)y xs(y x ) y 0 s (x y)+ s(y x ) y y 0 s ( s ) + s s x xy y 0 s y yy 0 /s

30 xa y, y x<y, y y 0 +(-s)x xy, yy 0 /s xy, yy 0 /s y 0 y 0 a x / y s xy s y xy y<x<y, y y 0 ~ y0 s( s) + s~ a~() y s s x yf(x) y 0 y 0 0 x sy ay

31 y 0 yf(x) P P x > x, y > m m m y m y y 0 yf(x) 0 x 0 P ( x m, y m) P(x m,y m ) xg(y) x

32 yf(x) x 0 x xg(y)y P P x < x, y < m m m y y P ( x m, y m) y yf(x) 0 0 x 0 m P(x m,y m ) xg(y) x

33 (x, y) y P yf(x) y 0 y a y P P? P P? yf(x) P y 0 0 x 0 P(x m,y m ) xg(y) x

34 Discussions

35 8.

36 X, Y, y x,y() y o X,Y Xx 0, Y y 0, 0 x x o X,Y p(x,y) (x,y) (x 0 -x, y 0 -y) y. p x

37 (x,y )(x,y ) p, p p, p MN, y y o y y M. p M. p 3 (x 3,y 3 ). p N N 0 x x x o, X,Y x MNp 3 M N

38 y f(x,y)c f(x,y)c c c ~ y x. p f ~ 0 y. p x x (x, y) () p xy y x; p yx x y

39 g(x,y)c y g(x,y)c c fc gc ( x O y, AB ABp, ()ABp x y y o O O AB p A P gc B fc O x o y x x

40 ~ (x,y) 0 x x 0, 0 y y 0 X,Y AB x 0,y 0 (x 0,0), (0,y 0 ) CD Xa, Yb, ax+bys (sax 0 by 0 ) y. y o 0 D A p ABCD p B. x C x o

41 Discussions

42 9.

45 6 4

46 3 7 < π < 7 sin θ < θ < tanθ θ π < π <

47 < π <

49 656Wallis 0 k k k k k k π π 0 k π

50 ) ( 5 3 arctan k x x x x x k k k ), ( + x x ) ( k k k π

51 0 k π 0 k π

52 π arctan arctan + arctan 4 3 C A B D arctan arctan 3 arctan A B + C C D

53 Machin π 4arctan arctan (Machin π α arctan β 4α tan β

56 π 4 x dx 0 π 4 dx 0 + x

57 Discussions

(p.29). (a) F Qq r 2 ()() N (b) Q 2 r 2 F ( 2 )() Q 0 5 C 2. (a) F (b) F 3. 7 (p.42). (a) T (b) F (c) T 2. (a) A (b) (c) 4. (a) 4 (b) (

(p.29). (a) F Qq r 2 ()() N (b) Q 2 r 2 F ( 2 )() Q 0 5 C 2. (a) F (b) F 3. 7 (p.42). (a) T (b) F (c) T 2. (a) A (b) (c) 4. (a) 4 (b) ( 20 (p.7). (a) T (b) T (c) T (d) F 2. B 3. 3 (p.4). D 2. C D A B D B D B D 3. (a) F (b) F (c) T 4. 2 (p.0) 4 (p.23). (a) B (b) A P 2. (a) F (b) T 3. 4. 5. 6. (a) (b).6 0 9.6 0 9 0 0. (a) X Y (b) X Y Z 2.