ΑΛΓΕΒΡΑ Β΄ Γενικού Λυκείου

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ΑΛΓΕΒΡΑ Β´ ΓΕΝΙΚΟΥ ΛΥΚΕΙΟΥ
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Transcript of ΑΛΓΕΒΡΑ Β΄ Γενικού Λυκείου

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2. : . . : 1991 : 1992, 1993, 1994, 1995, 1996, 1997, 1998, 2012 . 3. . , . , . . , . 4. . (2010) , - . , . , . , . . . : , (2010), - . , . , . , . . . - (2010), - (2010). : 1 , -, . , . 2 , , , - . 3 - . , -, . - . 4 . 5 , . 5. 1 : 1.1 .......................................................................9. 1.2 ...............................................................24 2: 2.1 -- . ...........................30. 2.2 - ............................40 3: 3.1 ...................................................49 3.2 ...........................................60 3.3 1 .......................................................65 3.4 ...................................................73 3.5 .............................................83 3.6 ............................89 3.7 2.......................................97. 3.8 ...................103 3.9 f(x)=x+x...................................................108 3.10 ........................................................................ 114 4: - 4.1 ...................................................................................128 4.2 .................................................................132 4.3 .....................................140 . 4.4 ........150 5: 5.1 ....................................................................160. 5.2 ....................................................................................173 5.3 ..............................................................181. . ........................................................193 - ....................................195 6. 1 1.1 x + y = x + y = , 0 0, , . : : 0, , : x + y = y = x + y= x+ , - = yy . yy x+y=, =0x+y=, 0 0x 0 x : 9 0, (. ), 7. 10 1: 9 = 0 , y = xx yy (. ). y = 0 ( 0 ), x+y=, =0 x = x = . - 0x yy xx . y y :1y= x1 9 x 2y = 2 2 1 x+y=, =0 y=x 1 2 1y = y 0 1x 2 0 2x y= x1 2 yy 1 . -1 2 y=2yy 1 02 y= x1 x 2 9 y=2 -1 0x xx -2 y=2 yy 2 . 02x-1 0x y9 x=2 yy - x=2 xx 2. y 0 2 x=2x . 02 x 8. 1.1 11 , (4,-1) x 2y = 6, 4 2(1) = 4 + 2 = 6. , , (16,5),(10, 8) 1 k, k 3 , k . 2 2 x 2 x+y= x+y= , - , , 2 x 2 x + y = x + y = . . . . : . () () , .. (), () + ( ) , () - 0, () . () + ( ) () (). - 1o : 9 0, : = = 9 = = , + = +., , : x 2y =(1)6 3x + 4y =(2) 8 9. 12 1: , ( ) , .. (1) x. = 2y + 6x3x + 4y = 8 x 3(2y + 6) + 4y = 6y + 18 + 4y =88 10y = 10 y =1 = 2y + 6x y = 1 y : x = 2(1) + 6 = 4 (4, 1). , . - , . , x = 4 y = 1, :1 : 4 2(1) = 62 : 3 4 + 4(1) = 12 4 = 8 ( ) , : 10. 1.1 13 x 2y 6 (3)= 3x + 6y =18 = 8 13x + 4y3x + 4y =8 , - , :3x + 6y + 3x + 4y = 18 + 8 10y = 10 y = 1 . : x 2(1) = 6 x + 2 = 6 x = 4 . (4, 1) ( - ). 2 x 2 x 2y =6 3x + 4y =8 . , - . y 3x+4y=8x2y=6OA(4, 1)x, x + y = x + y = , , . 2 x 2 . , 2 x 2 , , , . 11. 14 1: 2 x 2 -. : 2 2x + 3y =3 y = x +1 39 = , 4x 9y 1 y4 1 = x 9 9 , . y , 2 1 1(1, 0,3) . , 0 1x - (1, 1 ) .3 x + 2y =3 y9 2x + 4y = 51 1 3 y= x+x 2 2 0 , ,21 y = x 5 2 4 . y1 y + 1 = 2x9 4x 2y = 2 2= 2x 1 y x , 0= 2x 1y , . (k, 2k 1), k . 12. 1.1 15, 2 x 2 :9 9 9 . 2 x 2 - 2 x 2 . x + y = x + y = 0 0. - : y = x + (1 ) y = x + ( ) 2 1 2 - 1 = 2 = , 0 , 1 2 , x + = x + x = ( )x = x= : + + y = + = ( )( )=( ) 13. 16 1: y = , , (x, y) = , = , - =0 , 1 2 , . . =0 =0. x + y = x + y = : 0 (x, y) = , = 0 . , D= : D= = . D, x , : . Dx = = , D, - y , : .Dy = = 14. 1.1 17 - , , : x + y = x + y = Dx D D0, , (x,y) x = y = yD D D=0, . : x 2y =69 3x + 4y =81 2D==1 4 3(2) = 4 + 6 =10 0, 3 4 . 6 21 6 + 16 = 40 D y = = 18 = Dx = = 24 8 10 8 4 3 8:D y 10 D x 40x== = 4 y === 1 .D 10 D10, (x, y) (4, 1) .=2x 3y =409 4x 6y =802 3D= = 6) 4(3) =12 + 12 =2( 0 4 6 - . 2, 2x 3y =40 =, 2x 3y 40 2x 3y = 40. 2x 402x 3y = 40 y = .3 15. 18 1: 2k 40 k, , k 3 3x + y = 119 9x + 3y =63 1 D== 99 = 09 3 . 3x + y =113x + y =2 .1 x y = 1 2 x 2y = - , . , . , . , . D, Dx, Dy. : 1 D= 2 = 2 + 2 = ( 2) 2 1 1 Dx == 2( 1) + = 2 2 1 Dy = 2 = 2 2 ( 1) = 2 (1 + 1) = 2 (2 ) 16. 1.1 19 , D = 0 . : 2)= 0 =0 =2D = 0 ( : 9 D0, 0 2, (x, y), : Dx 2 ( 2) 1=x = = = 2) D ( 2) ( D y 2 (2 ) 2 ( 2) = .y== = D( 2)( 2), 0 2 , 1 , . 9 D = 0 , = 0 = 2 , . : = 0 , 0x y = 1 y = 1 0x = 0 = 02y y . = 2 , 2x y 1=2x y 1= 4x 2y 2 = 2x y 1= . , y = 2x 1 ,2x y =1 ( k, 2k 1) , k . 3 x 3 x+y+z=0 , - , , , . . 2x+3y+z=6 - (2, 1,5) , 22+3(1)+5=6. 17. 20 1: :1x + 1 y + 1z = 1 , 2 x + 2 y + 2 z = 2 3 x + 3 y + 3 z = 3 , - , , 3 x 3 1x + 1 y + 1z = 1 2 x + 2 y + 2 z = 2 x + y + z = 33 33 - 2 x 2 . 2x y + 3z = 9(1) x + 3y z =10 (2) 3x + y z = 8 (3) . , .. (3) z, - . : 3x + y z = 8 z = 3x + y 8 (4) (1) (2) :9 2x y + 3z = 9 2x y + 3(3x + y 8) = 9 11x + 2y = 15(5)9 x + 3y x + 3y (3x + y 8) = 10 x + y = 1 z = 10(6) (5), (6) 11x + 2y = 15, x + y =1 x=1 y=2 . x y (4) z = 3. (1, 2, 3). 3 x 3, , 2 x 2, 3 x 3 . 18. 1.1 21 x y =41. x + y =2 i) ii) .2. x y x 1 y 2 = = i) ii) 3 7 84 x + y = 454x + 3y =83. : x 5 2y + 1 2x 1 y+2 2 + 7 +2= 0 3 = 4 4 i) ii) x + 6 y 6 =8x +3 3 = y x 3 2 2 34. : x 3y =3 2y= x + 2 i) ii) x1 3 y =2 2 x y +1 = 05. : 2x + y = 7 2y 3x 8=i) ii) 3x 5y = 4 x + 3y + 1 =06. , . 2x 5y =42x 3y = 40 3x + y =11 i) ii) iii) 6x + 7y =1004x 6y = 80 9x 3y = 27. : ( 3 + 1)x + 4y = 7 ( 3 1)x + 2y = 2 i)ii) 1 x + ( 3 + 1)y =1 3 x + ( 3 1)y = 1 2 19. 22 1: 8. : y x + 2 = 3 3x 2y =11 5x y + 3 = 42 i) 2x 5y 2 =3 ii) x 3y + = 2 iii) 3x + y + = 5 5x + y 2 =33 3x 2y + 2 = 22 5x + 3y 2 =16 y 1. i) 11 1 2 . 2 ii) 1 2 ;O1 4x1 2. 26 , 68 . ; 3. 1,5 4. 2200 - 5050 . . 4. R T R =T + . 20 C 0,4 80 C 0,5 , . 5. , 50% 80% . 100 ml - 68% ; 6. 1 : 2x + 4y = 2 : x + 2y = . 3 ,i) 1 2 . ii) - ; iii) ; 20. 1.1 237. : i) 1 : x + y = 2 2 : x + y =1. ii) 3 : x y = 2 : x + y =1.8. : ( 1)x 2y =1 ( 2)x + 5y =5 i) , ii) , 4x ( + 1)y = 2 x + ( + 2)y =5 9. 3 1 2 =6 , O1O3 = 5 O2O3 = 7 . 1 2 .10. , . N = x , B = y = z , - , .11. . 50% , 10% 30% . 52 lit 32% , - - -. .12. -, y = x 2 + x + . - . y yy K(1,4) 3y=g(x)4y=f(x) y=h(x)O x1Ox O 2 4 K(2, 1)x 21. 24 1: 1.2 , -. , 13 89. x, y , x + y = x 2 + y 2 =. - 1389 , :x + y = 13 (1) 22 x + y = (2) 89 : (1), , .. x , (2). x + y = 13 y = 13 x (3). 2 22 2 x + (13 x) = 89 x + 169 26x + x = 89 2x 2 26x + 80 = 0 x 2 13x + 40 = 0. 2 = 9 . :813 3 = = x 2 5 (3), x=8 y=5 , x=5 y=8. (8, 5) (5, 8). 5 8. , , . x + y = (1)51 . xy = 6 (2) 22. 1.2 25 (1) x (2). : y = 5 xx + y =5 (3). xy =6 x(5 x) =6 5x x 2 =6 x 2 5x + 6 =0 x 2 = 3.= x (3) x=2 y=3 , x=3 y=2 . (2, 3) (3, 2) . 5 6. , Vieta 2 5 + 6 = 0 . 2 3 (2,3) (3,2). x+y=5 , xy=6 6 y = . - x . y A B 1 O 1 x 23. 26 1: (2,3) (3,2) . (2,3) (3,2) .2 xy = 6 (1) 2 2 x + y = (2)13 (1) x (2). 6xy = 6 y = x (2) : 2x 2 + y 2 = 13 x 2 + 6 = 13 x 36 x2 + 2 =13 x x 4 + 36 = 213x x 4 13x 2 + 36 = 0 . x 2 = , 2 13 + 36 = 0 , =9 =4 .9 =9 2 x =9 x =3 x = 3 (1) x=3 y=2 x = 3 .9 = 4 x 2 = 4 x = 2 x = 2 (1) x=2 y=3 x = 2 y = 3 . (3,2), (3, 2), (2,3) (2, 3). 6 xy = 6 y =, - x2 2 x + y = (0,0) = 13 .13 24. 1.2 27 . y A B 1x BA x 2 + y 2 + xy =31. : . x + y =12. : y = 3x 2x 2 + y2 = 9 x 2 + y2 = 5 i) ii) iii) 12x 3y = 4x y =0 xy = 2 .13. S = 0 t + t 2 = 0 + t , + 0 2= S t . 2 x 2 2y + 10=1. o 22 - .x + y =25 25. 28 1: 2xy y 2 5y = 0 2. : 2 y = x 4x + 3 3. 120cm2 . 3cm , 2cm , . -. 4. y = x 2 y = + k, k . - 2x k . 2y = x 2 5. o . y= x + 1 I. : x + 2y =1 x + y = 1 2x + 4y =2x y = 1 (1 ) : ( 2 ) : ( 3 ) : ( 4 ) : 2x + 4y = 0, x + 2y = 4, 1, x + 2y = 2 x + y =1 , , . ) , ) , ) . (1) (2) (3) (4) II. , , .1. , . A2. D = 0 , . xy = 13. . x + y =04. x 2 + y 2 = = x 2 + 1 1 y . A 26. 2 . . 2.1 -- T = f (t) t (t =0) (t =24).T(C)11T=f(t) 5 3 4 16 24 t(h)) [4,16] .T(C) 11T=f(t)5f(t1) f(t2) 4t1t216 24 t(h) 27. 2.1 -- 31 , , - , t1 , t 2 [4,16] t1 < t 2 : f (t1 ) < f (t 2 ) T = f (t ) [4,16] . : f - , x1 , x 2 x1 < x 2 :f (x1 ) < f (x 2 ) f f . , f (x) 2x 3 . = x1 , x 2 R , x1 < x 2 . :x1 < x 2 2x1 < 2x 2 2x1 3 < 2x 2 3 f (x1 ) < f (x 2 ): f (x) = x + , > 0 .) , [16,24] .T(C) T=f(t)f(t1)5f(t2) 416 t1t2 24 t(h) 28. 32 2: , , - , t1 , t 2 [16, 24] t1 < t 2 :f (t1 ) > f (t 2 ) T = f (t ) [16,24]. : f , x1 , x 2 x1 < x 2 : f (x1 ) > f (x 2 ) f f , f (x) = + 5 . 2x x1 , x 2 , x1 < x 2 . : x1 < x 2 2x1 > 2x 2 2x1 + 5 > 2x 2 + 5 f (x1 ) > f (x 2 ): f (x) = x + , < 0 . . T = f (t). T(C) 11T=f(t) 5 3 O 416 24 t(h) 29. 2.1 -- 33 :) t1 = 4 , f (4) = 3 . :f (t) f (4) = t [0, 24]3 , T = f (t) t = 4 -, f (4) = 3 . : f, , x 0 A () :f (x) f (x 0 ) , x A x 0 A , f (x 0 ) f min f (x) . , f (x) 3x 4 + 1 . = x 4 0 , x , 3x 4 0 , x , 3x 4 + 1 1 , x .: f (x) f (0) , x ., f x 0 = 0 , f (0) = 1) t 2 = 16 , T(16)=11 . : f (t) f (16) = t [0, 24]11 , T =f (t) t =16 , f (16)=11. : f, , x 0 A () :f (x) f (x 0 ) , x A 30. 34 2: x 0 A , f (x 0 ) - f max f ( x) . , f (x) = 4 + 1 . 3xx 4 0 , x , 3x 4 0 , x , 3x 4 + 1 1 , x .:f (x) f (0) , x , f x 0 = 0 , f (0) = 1 . () () . (. ) (. ) (. ) (. ). yy y=f(x)y=f(x) 1 1 1x 1 x y y1y=f(x)1 y=f(x) 1x 1x 31. 2.1 -- 35 y) - Cf f -My M . Cff(x) f(x) yy, x O x x Cf Cf yy Cf ., , M(x, y) Cf yy M ( x, y) M(x, y) M ( x, y) Cf , y = f (x) y = f (x) , : f ( x) = f (x) f . : f, , , x A : x A f ( x) =f (x) yy. , f (x) = 2x 4 x 2 + 1 , x : f ( x) = 2( x) 4 ( x) 2 + 1 = 2x 4 x 2 + 1 = f (x), yy . y) -Cf M Cf f y .f(x) Cf x x O x , -f(x) Cf -y M Cf . 32. 36 2: , , M(x, y) Cf M ( x, y) M(x, y) M ( x, y) Cf , y = f ( x) y = f ( x), :f ( x) =f (x) f . : f, , , x A : x A f ( x) =f (x) . , f (x) 2x 3 x , = x : f ( x) = x)3 ( x) =2x 3 + x =f (x) 2( , .: y = x 2 ,y = x 4 , y = x 6 ., , yy , , - y = x , y = x 3 , y = x 5 ., , , . - f [6,6]. f : 33. 2.1 -- 37) f : i) , ii) , iii) .) f , - . y 1x f , yy . , yy f, - f, ().A A 4 B 6 5 225 6 x :) f : i) [0,2] [5,6], ii) [2, 0] [6, 5], [0,2] [5,6] f . iii) [5, 2] [2,5] . 34. 38 2: ) f 4 x 6 6. :max f (x) = f (6) = f (6) = 4 f 0 x 0. : min f (x) = f (0) = 0. 1) - : ) ) .yy yy=f(x)y=g(x) y=h(x) x 2 x1 1x122 2) - , . 3) : i) f (x) = x 2 6x + 10 x=3. 2x ii) g(x) = 2 x=1. x +1 4) : i) f1 (x) 3x 2 + 5x 4 ii) f 2 (x) 3 x + 1 = =iii) f 3 (x) x + 1= 35x22x iv) f 4 (x) x 3x v) f 5 (x) = = vi) f 6 (x) = . 1+ xx2 +1 35. 2.1 -- 395) :1 i) f1 (x) = ii) f 2 (x) =x2iii) f 3 (x) = x 1 x + 1x1x+ iv) f 4 (x) = 2 x v) f 5 (x) =x vi) f 6 (x) = 1 x2 . x +16) .y yy y=f(x) y=g(x) y=h(x) x x x7) y yy y=f(x) y=g(x) y=h(x) x x x8) - ) ) .y yyC1C2C3 x x x 36. 40 2: 2.2 - ) f (x) x + 1 . = x + 1, x < 0 f (x) = , x + 1, x 0 - y f (x) x + 1 , -= y=|x|+1 1 19 y = x + 1 , x 0 119 y= x + 1 , x 0 ,1 y=|x| 1 x O 1x yy x Oy xOy , , (x) =(). x, (x) = -x 1 , (1) f (x) x + 1 . , , ,= :f (x) = + 1 , x ,(x) x f (x) 1 (x) .: f , : f (x) = + c , c > 0 ,(x) c ( )(1) yy . 37. 2.2 - 41 yy=(x)+c ccc ccOxy=(x) ) f (x) x 1 . = x 1, x < 0f (x) = , x 1, x 0 yf (x) x 1 , = y=|x| 119 y = x 1 , x 0 1 19 y= x 1 , x 0 ,O 1 y=|x|1x 1 yy -1 x Oy xOy (x) =().x, (x) = -x 1 , f (x) x 1. , , , := f (x) = 1 , x , (x) x f (x) 1 (x).: f , : f (x) = c , c > 0 , (x) c ( ) 38. 42 2: yy=(x)O cxcc ccy=(x)c ) f (x) x 1 . = x + 1, x < 1f (x) = , x 1, x 1 f (x) x 1 , =y 119 y = x + 1 , x 1 y=|x| y=|x|19 y= x 1 , x 1 ,1 1 1 xx -Ox x Oy xOy (x) =().x, (x) = -x 1 , (2) f (x) x 1 . , , ,= f (x) =(x 1) , x , f (x) x 1 x =(x) = x 1. x(2) xx . 39. 2.2 - 43: f :f (x) =(x c) , c > 0 , c ( ). f (x) =(x c) , f x x c , c x. , f c ( ).y c cC Cf (x-c)f(x) cc xcx O x ) f (x) x + 1 . = x 1, x < 1 f (x) = , x + 1, x 1 yf (x) x + 1 , = 1 y=|x|19 y = x 1 , x 1 9 y= x + 1 , x 1 ,1 1y=|x+1| 1 xx - 11 Ox x Oy xOy (x) =().x, (x) = -x 1 , - 40. 44 2: f (x) x + 1 . , , , = f (x) =(x + 1) , x , f (x) x + 1 x = (x) = x +1. x: f , :f (x) =(x + c) , c > 0 , c ( ). f (x) =(x + c) , f x x + c , c x. , f c ( ).c yc Cf Cc f(x) =(x+c) cOx x+c x f (x) = x + 3 + 2 . y x + 3 , -= y = x 3 . - y = x + 3 + 2 , y x + 3 2= . 41. 2.2 - 45, - yf (x) = x + 3 + 2 - - y=|x+3|+2y=|x+3| y = x , - 3 y=|x| -2 2 ().3O 1 x: , - :f (x) =(x c) d , c,d > 0 , - . A 1. - :(x) = x ,f (x) x + 2 = g(x) x 2 .=2. :(x) = x ,h(x) x + 2 = q(x) x 2 .=3. :(x) = x ,F(x) = x + 2 + 1 G(x) = x 2 1 . 42. 46 2: 4. i) f (x) = 2x 2 4x + 5 f (x) =(x p) 2 + q - g(x) = 2x 2 f. ii) f (x) = 2 + 8x 9 , -2x2 g g(x) = 2x . 5. 1 O(0,0) A(2,0).yCO x - : i) f (x) = + 2 g(x) = 2(x) (x)ii) h(x) =(x + 3) q(x) =(x 3) iii) F(x) =(x + 3) + 2 G(x) =(x 3) 2 . 6. (x) = 2x 2 1 . - f :i) 2 1 . ii) 3 2 .iii) 2 1 .iv) 3 2 . 43. 2.2 - 47 2 I) - , , - .1. f , f . 2. . 3. (1,2) , (2,1) (3,3) . 4. f 1, f (0) < 0 . 5. f - (1,2) (2,5) , f . 6. f 1, f (x) = 2 . 7. f :[1, 2] f (x) = 3x 2 . 8. , . 9. f , f - . 10. f , f . II) f. f, 3x 4(x) = , 1 2 , : ) f (x) = 3(x 1) 4 + 2 ) f (x) = 3(x 1) 4 2 ) f (x) = 3(x + 1) 4 + 2 ) f (x) = 3(x + 1) 4 2 44. 3 3.1 . - - MM1 NN1 , 1 1 O M M1 O N N1 , :(MM1 ) (NN1 ) (OM1 ) (ON1 )(MM1 ) (NN1 ) = ,= = (OM)(ON)(OM) (ON) (OM1 ) (ON1 ), (MM1 ) (OM1 )(MM1 ), (OM) (OM) (OM1 ) , - . , , , , , . , M1 O M , : =(MM1 ) (OM) ( ) 45. 50 3: = (M1 ) (OM) ( ) =(MM1 )(OM1 ) ( ) , - , = (M1 ) (M ) 1 ( ) , 00 3600 Oxy , Ot Ox - Ot (. , ). Ox , Ot .yt y t(x,y) 22 (x,y) y x 1 x 1x (x, y) M1 xx (. ). (. ), , , :(MM1 )(M1 )(MM1 ) (M1 ) = , = , = = (OM) (OM)(OM1 ) (M1 ) (1 ) = x , (1M) = (OM) = x 2 + y 2 = > 0 . ,y : y xy x = , = , = = , = x 2 + y2 > 0 . x y 46. 3.1 51 , - ( ). : = y ,y ( x0) = ,=x x 2 + y2 > 0 = x , =x ( y0) y (x, y) ( ) = x 2 + y 2 > 0 . 360 y Ox - Oxy -t . 300 x300 , Ox = 360 + 30 390. =390 0 360 , - : = 360 + , N* 00 < 3600 y Ox, 390 0 , - 30 , 300x Ox -t 360 + 30 = 390: = (360 + 30 ) = 390. 47. 52 3: -: = ( 360 + ), N 0 < 360 360 , , 0 360., , , : = y ,y ( x0) = ,=x x 2 + y2 > 0 = x , x ( y0) = y (x, y) ( ) = x 2 + y 2 > 0 . ( ) Ox . Ox , , - , 360 + , . Ox , , , 360 + , - . , k 360 + , k , ., k : (k 360 + ) = , (k 360 + ) = (k 360 + ) = , (k 360 + ) = 48. 3.1 53 , , , . - , - . (0,0) y - o 100o 90 80 o 110 o70 o =1 - 120 o60 o 130 o50o . 140o40o - 150o N(,) . 160o 20 o 170o 10 o - x 0,1 350180o x , .. -0,1 350 o190 o =35 , 200o 340o (, ). 210 o330 o 220 o 320 o y 310o (x,y) 35 = =1 240o o 250 290o300o o 260 270o 280o 35 = 0,57., 35 = =1, 35 = 0,82., (x, y), : = x = = y = xx , yy . :1. , 1. : 1 1 1 1 49. 54 3: 2. , , . 10 20 3040 ++ ++ ++ ++ -y tB M(x, y). E(1,yE ) M - .A OAx 1 , B ( ) ( ) = == ( ) () 1 yE , (AE)= yE , = yE. . : = yE = , x =1 , . 50. 3.1 55 B . , AB (, ) ( 1rad), 1rad . , O A ( rad) S = . - : ( 1 rad ) , - , ( 1 rad). - , : , rad . - 2, 360 2 rad., 360 1 rad , 2, 180 rad .180 , = , : = 180 :9 60 , = = 600 180 = = 180 3 60 = rad.3 51. 56 3: 59 rad , 6 5= = 180 6 565 === 150 180 6 1805rad=150. 6 - . rad 00 010 1 333036 2232245 1 14 223 1 3 3603 22390 1002 , x rad x, (x rad), ( x rad), (x rad) (x rad), x, x, xx. , .. rad 33 (100rad ) 100 . 52. 3.1 571 h , . . :hh48 = , = 48hh70 = , = 70 = = 20m h h 2070 4820, h = = . 48 7070 48 70 2, 75 48 1,11. (1) :61, 05h 37 1, 64 37m .2 750o . 750 360 2 30, 750 =360 + 30 2 1 3750 = (2 360 + 30 ) = 30 = 750 = 30 = 22 3 750 = 30 =750 = 30 = 3 3 53. 58 3: 793 rad. 3 79 79 = 2. 79 6 3 679 79 113 1. = 2 13 + 2 13 2 + ,= =36 63 : 79 379 1= 13 2 + = = = =3 3 32 33 2 79 793 = = 3 = =3 33 3 3 A 1. 6 y x x, y . 300B3 A 4 2. .60 0 300B2 3. S = 6cm. , : i) = 1cm ii) = 2cm iii) = 3cm . 4. rad i) 30 ii) 120 iii) 1260 iv) 1485. 5. :591 i) rad ii)rad iii) rad iv) 100rad . 10 6 3 6. i) 1830 ii) 2940 iii) 1980 iv) 3600. 54. 3.1 59 1. -N (N) h , - 70 0 1000 - () () 1.000 (1 0,3 m) . . i) h = 30 , 45 60. ii) , h=1000 ;2. :i) : () = () = 2 45 = 2. ii) ()= 4 22,5.iii) (). 22,5 o 45oA B3 iv) , 31 1 , () 2 2 2 .= v) 22,5.vi) ;A3. 30 0 . 6 30 0B4. 1mm . - . 55. 60 3: 3.2 . . :1. 2 + 2 = 1 M (x, y) , :x = y = yt ,(x,y)y2 2(OM) =1 ( )= x + y= x 2 + y 2 2|y| 1 : 22A A x + y = 1, x |x| O x : 2 + 2 = 1 2. == : y = =( x = 0 ) x x ==( y = 0 ).y 56. 3.2 61 (1) (2), - .3. . = 1: = =( 0 0) : = = 1. 12 4. 2 = 2 = 1 + 2 1 + 2 i) 2 + 2 = 1 2 0 : 2 2 1 21 1 2 + = 22 = +1 2 2 =. 1 + 2 1 2 = . 1 + 2 1ii) 2 + 2 = 1 2 = , 1 + 2 112 : 2 + = 1 2 = 1 2 = .1 + 2 1 + 2 1 + 2 2 2 = . 1 + 2 57. 62 3: 51 = 90o < < 180o, -13 . 2 + 2 = 1 2 = 1 2 . 5 :13 22 5 25 169 25 144 = 1 = 1 = = . 13 169 169169 90 < < 180 , < 0 , :144 12 = = 169 13 = =, : 512 5 12 = 13 = = 13 = . 12 125 5 13132 4 4224 42 i) + = 1 2 ii) = 2 1 i) : 4 + 4 = ( 2 ) 2 + ( 2 ) 2= ( 2 + 2 ) 2 2 2 2 = 1 2 2 2 ,( 2 + 2 = 1 )ii) : 4 4 = ( 2 ) 2 ( 2 ) 2 = ( 2 + 2 )( 2 2 ) = 2 2 ( 2 + 2 = 1 ) = 2 (1 2 ) = 2 2 1. 58. 3.2 63 3 1. x = < x < , - 5 2 x rad. 23 2. x = < x < , - 3 2 x rad.3 3 3. x = < x < 2, - 3 2 x rad.2 5 4. x = 0 < x < , - 52 x rad.3 5. x = 2 < x < 2, - 22xx . 1 + x 6. , x : i) x = 0 x = 0. ii) x = 1 x = 1. 34 iii) x = x = . 557. , M ( x, y) x = 3 y = 3, O(0,0) = 3. 8. x = 2 y = 3 , 9x2 + 4y2=36.9. x = r , y = r z = r , x2 + y2 + z2 = r2. 10. : 1 442 i)=ii) = 2 1 . 1 + 59. 64 3: 11. : 1 + 2xx 2 i)+=ii)+ = .1 + 1 x 1 + x x 12. : + i)= ii) 2 2 = 2 2 . + 13. :x x 1 i)+ = x + x ii) (1 x) 1 + = x x 1 x 1 x x 1 1 1iii) = x x iv) x x = x x.x + x x x B 1. x + x = , -: 1 1 i) x x ii) +x x iii) x + x iv) 3 x + 3 x. 2. : i) 4 x + 4 x = 1 2 2 x 2 x ii) 6 x + 6 x = 1 3 2 x 2 x. iii) 2( 6 x + 6 x) 3( 4 x + 4 x) - x , . 1 + x 1 x 3. < x < , = 2x.22 1 x 1 + x1 + x + 1 x 1 + x x 4. 0 x < , = =.21 + x 1 x x 1 x 60. 3.3 1 65 3.3 10 , , 0 90. . yt ,(x,y) = , , - , A A xx. x .(x,y) , - t : () = () = () = () = : . :9 : 1 3 (30 ) = (30 ) = (30 ) = (30 ) = 2 23 (30 ) = (30 ) = (30 ) = (30 ) = 3 3 9 , : 2 2 = = = = 442 4 42 = = 1 = = 1 4 4 44 61. 66 3: 180 - y B 180 , = 180 , t t, , (x,y)(x,y)180 0 yy . A A x. , - :B (180 ) = (180 ) = (180 ) = (180 ) = : 180o . :9 150 180 30 , :=1 150 = (180 30 ) = 30 =23 150 = (180 30 ) = 30 = 2 3 150 = (180 30 ) = 30 = 3 150 = (180 30 ) = 30 = 329 = , : 33 2 3 = = = 3 3 32 62. 3.3 1 67 2 1 = = = 3 3 32 2 = = = 3 3 33 2 3 = = = 3 333 180 yB180 , = 180 + , ,t , -(x,y) 1800+ . -A Ax .(x,y) - t , :(180 + ) = (180 + ) = (180 + ) = (180 + ) = : 180o -, . :9 210 180 + 30 , := 1 210 = (180 + 30 ) = 30 = 2 3 210 = (180 + 30 ) = 30 = 2 3210 = (180 + 30 ) = 30 = 3 210 = (180 + 30 ) = 30 = 3 63. 68 3: 49 = + , : 33 4 3 = + = = 3 332 4 1 = + = = 3 332 4 = + = = 3 3 3 3 4 3 = + = = 3 3 33 90 - y t 90 , 90 , , = B y=x (y,x) , t (x,y) xOy . 90 0 A OA x . , - B : (90 ) = (90 ) = (90 ) = (90 ) = , 90o , - . , 60 90 30 , := 3160 = 30 = ,60 = 30 =,2 2360 = 30 =3 60 = 30 = 3 64. 3.3 1 69 , 0 90.1+ 51 36o = . 4 54o. 54 90 36 , =1+ 554 = 36 =4 2 + 2 = 1 2 54 + 2 54 = 1, : 2 2 2 1+ 5 6 + 2 5 10 2 5 54 = 1 54 = 1 4 = 1= , 1616: 10 2 5 54 =4 :541+ 5 5410 2 554= = 54 = =. 54 10 2 554 1+ 52 - : ) 90 + , ) 270 ) 270 + i) 90 += 90 (), : (90 + ) = (90 ()) = () = . 90 + . 65. 70 3: ii) 270 180 + (90 ) , : = (270 ) = (180 + (90 )) = (90 ) = . 270 .iii) 270 + 360 90 + 360 + ( 90 ), : = = (270 + ) = ( 90 ) = (90 ) = . 270 + . 1. : i) 1200 ii) 2850.2. 187 21 i) rad ii) rad. 6 43. : i) = ( + ) ii) + ( + ) = 0 ++ iii) = iv) = . 22 2 24. () (180 + ) .() (90 + ) 9( x) (2 + x) + x 5. : 2 = 1. 21(13 + x) ( x) x 26. : 2 ( x) + ( x)(2 x) + 2 2 x .2 66. 3.3 1 71 1. : 495 120 + 495 (120 ) .(120 ) + 495 2. : 5 7 (5 + ) (7 ) + 2 2 = 2 1. 5 7 (5 + ) (7 ) + 2 2 3. x + + x = 5, -36: 2 x + 2 + x . 3 6 4. :( + x) 00 , x A : i)x + T A, x T A ii) f (x + T) = f (x T) = f (x) f. , , 1 1. - . . - , , , ., f (t) = t, t . - .: x (x rad) . x = (x rad) ( + 360 ) = ( 360 ) = , x :(x + 2) = (x 2) = x 2. . 70. 3.4 75 x = (x rad). 2. , :x x =x :1={x x 0} x 1 (x + ) = (x ) = x, . , , :x x = x :2={x x 0} . f(x) = x f(x) = x 2, 2, . [0,2]. x xrad . - , , . :y x 0 B M , . 2 M , -x radx f(x) = x O A 0, . 2 f(x) = x : 71. 76 3: , 2 3 , 2 3 , 2 2 x = , = 1 22 33 x = , = 1.2 2 : 3x0 2 22 x 01 010 . . . : 3 53 7 x 0 4 24 4 24 2 x 2 0 0, 71 1 0,71 0 0,71 1 0,71 02 . [0, 2]:yy = x0x2 1 5 3 7 4 2 4 2xO 3 4 2 41 72. 3.4 77 f(x) = x , 2, [2, 4], [4, 6] . [2, 0],[4, 2] . , .y 1.51 0.50x /2/2 3/2 2 5/20.5 11.5 . - x ( x) = x. f(x) = x 0(0,0) . f(x) = x f(x) = x 2, 2, .. [0, 2]. : 3 x 0 2 22 x1 0 1 0 1... - : 3 5 3 7x 0 422 424 2x 210,710 0,711 0,71 00,71 1 2 73. 78 3: y = x 0 x 2p .yy = x 0x21 3 54 4x0 3 7 2 4 22 41 f(x) = x 2, : y 1 y = xx 2 0 3253 74 2 2 22 1 . x (x) = x. f(x) =x - yy. f(x) = x f(x) = x , , .. , . 2 2 ( , , ). 2 2 x rad - . x .:y x 22 O x , . f(x) = x , . 2 2 74. 3.4 79 x x . 2 x = - 2 f. x 2 x +. x = 2 f.yy yBy B BB A AA AA O A xA OA xOM xOx B MEBEBB f(x)=x , - , :x 02 3 4664 3 2 x 3 3 0, 6 0 0, 6 1 3 1, 7 1 3 33 1, 7 - . f(x)=x . y = x2 x3 3 2 2 2 22 f(x)=x , ( 5.3: (x)=x . 75. 80 3: 1 f(x)=3x . f(x)=3x - (x)=x. 2, : f (x + 2)= 3 (x + 2)= 3 x = f (x) , x . f (x 2)= 3 (x 2)= 3 x = f (x), x . - f(x)=3x. y 3 23x 0 2 y = 3x y = x22 1 x x0 1 0 1 02 1 2 3 4 2 3x 0 3 0 3 0 32 f(x)=2x f(x)=2x , 2x 2, , x - . , f(x)=2x .:f (x + ) = 2(x + ) = (2x + 2) = 2x = f (x), x f (x ) = 2(x ) = (2x 2) = 2x = f (x), x . , - f(x)=2x.3 yy = 2x x0 14 2 4 x 3 3 2 2x 0 1 01 0 2 2 1 22 y = x3 f(x)=32x . 3, 3 . 76. 3.4 81 f(x)=32x :y 3y = 32xx0 3 4 2 4 32x 0 3 030 x 0 2 3 3 2 24 22 - . 3 , f(x)= x, ,>0: (i) , . (ii) 2 . f(x)= x, ,>0 1. , i) f (x) = 2x, g(x) 0,5 x, h(x) = 2 x, 0 x 2= ii) f (x) = 2x, g(x) 0,5 x, h(x) = 2 x, 0 x 2 .= 2. f (x) = x g(x) = 1 + x h(x) = 1 + x 3. f (x) = x g(x) = 3x, 0 x 2 . 4. f (x) = x g(x) = 3x,0 x 2 . x 5. f (x) = 2 . -2 ; ; f . 77. 82 3: x 6. f (x) = 2.2 7. i) f (x) = x ii) g(x) = 1 + xiii) h(x) = 1 + x . 8. f (x) = 2x. 9. f (x) = x. B 1. :y 1x 2y x 1 2y 1x 2y1 x 2y3x 2y 0.5x 2y2.5x 2 2. y= 3 t , y 6 t .i) - .ii) 0 t 12. 78. 3.5 83 3. 1m. , 1 h = 1 + 3t, 3t .i) - . 1m ii) iii) - 0 t 2 . 4. H x - x(t) =0,1+0,1.3t, t . i) .ii) 0 t 2 . 0,15m; 3.5 x=1 x = . 2 y = x 1 y = . 2y y= 12O 52 x6 6y=x x , f (x) = x -1 . 2, 2 x, (. ), 2 . 2, . 79. 84 3: - 1 5 x = [0, 2], = , 26 6 6 5 1 = = . 6 6 2 y 1 1x = M 2M 2 5/6 x /6 x= 2 + 6 OA , 5 x= 2 + 6, x = , = , : x= 2 + , x = 2 + ( )31 x = 2 3 3 =, ( ) = . 32 32 x = ( ), : 3 x= 2 3 , x = 2 + + 3 12 2x + = 4 2 1 = , 2x + = , 6 2 4 6 80. 3.5 85 2x + 4 = 2 + 6 , 2x + = 2 + 46 2x + = 2 + 2x= 2 + x= 466 424 72x + = 2 + 2x = 2 + x = + 466 4 24 x = 24, 7 x = +24 x = , 1.. x = . 2 - 1 x = [, ] , 233 1 = = .3 3 2 y 1x = M 2 3 1x x= 2 + 3 2 3 , M x= 2 3 81. 86 3: , x = , = , x= 2 + , x = 2 21 x =2 2 =, x = , 42 4 : x= 2 + 4 , x= 2 432 2x = 2 3353 =, = = . 6 2 6 26 25 2x = , 6 55 2x= 2 + 6 x = + 12 , , 55 2x= 2 x = 612 82. 3.5 87 x = x = 3. - y 3 . , , x , .. 2 2 , 2 2 , . , x = 3 . , = 3. 3 3 x = 3 : x = + , .3, x = , x = , :x = + , x = .1 x = 1 = 1, = 1. x = ,4 4 4 x = , 42 x = 3 = 3, x = , 6 6 x = + , 6 83. 88 3: 1. 22 i) x = 0 ii) x = iii) x = 0 iv) x = 222. 12 i) x = ii) x = 1 iii) x = iv) x = 122 3. 3 i) x = 0ii) x =iii) x = 1iv) x = 3 3 4. 3 3 i) x = ii) x = 3 3 5. i) (1 x)(2x 3) = 0 ii) (2x + 2)(1 x) = 0 6. i) ( 3 + x)(1 x) = 0 ii) (2x + 1)(2 x 3)x = 07. - i) x = 0,951 ii) x = 0,809 iii) x = 28,636 8. x 2x i) 23x = 3 ii) + 1 = 0 iii) 3 3=0 579. i) x + = 1 ii) 2 3x = 1 iii) 5x = 3 3 4 4 10. i) 2 2 + 1 = 0 ii) 2 2 x + 3x 2 = 0 iii) 32 t= 3 + 2 3t 11. i) 2 x + 5 2 x = 4 ii) x 2x = 1 12. x, : i) f (x) = 3 x , 0 x < 2, ii) g(x) = 7 x , 0 x < 2 2 2 84. 3.6 8913. ( - t) = 75 + 50 , S 6t o t = 1 . i) 100000 , ii) . 1. i) x + x = 0 ii) 2x + 3x = 04 3 2. 1 i) x x + 1 = x + x ii) 2x = 4 2 x 3. x = 1 (3,4). * 4. 1+x=x [0,2). 5. : x = + x [0, 2).3 3.6 , - M1 , M 2 (. 1). , - . (. 2).y yM 2 (, )M((-), (-)) M 1 (, )-- xxO (1,0)O(1,0) . (1). (2) 85. 90 3: , M1 , M 2 , : 1: 2: : 1 0 : ( ) ( ) M 2 OM1 = AOM = , (M 2 M1 ) = (AM). (M 2 M1 ) 2 = (AM) 2 : (P1P2 ) =(x 2 x1 ) 2 + (y 2 y1 ) 2 , P1 (x1 , y1 ) P2 (x 2 , y 2 ), : (M 2 M1 )2 = ( ) 2 + ( ) 2 = 2 + 2 2 + 2 + 2 2= 2 2( + ) ( )2= [( ) 1]2 + [( ) 0]2 = 2 ( ) + 1 2( ) + 2 ( )= 2 2( ). ( 2 1 ) 2 = ( ) 2 2 2( + )= 2 2( ) + = ( ):( ) = + (1) , , 0 < < 3600 , , . , :( ()) = () + () = :( + ) = (2) 86. 3.6 91 (1) (2) - , - . , : 15 = (45 30 ) = 45 30 + 45 30 2 32 12( 3 + 1)= + =2 22 24 75 = (45 + 30 ) = 45 30 45 30 2 32 12( 3 1)= =2 22 2 4 (1), , - . x = x x = x, : 22 ( + ) = ( + ) = ( ) 2 2 = + = + 22 :( + ) = + (3) : ( ) = , : 15 = (45 30 ) = 45 30 45 30 2 32 1 2( 3 1)= =2 22 24 75 = (45 + 30 ) = 45 30 + 45 30 2 32 1 2( 3 + 1)= + =2 22 2 4 87. 92 3: - + , , . , : ( + ), , ( + ) 0, 0 0. : ( + ) + ( + )==( + ) 0 + + = =1 : + (5)( + ) =1 , : (6)( ) =1 + : 1( + ) = (7) + 1 ( ) = (8) + , :31 45 30 3 = 3 3 15 = (45 30 ) = =1 + 45 30 3 3+ 31+ 3 (3 3)(3 3) 12 6 3 = = = 2 3 (3 + 3)(3 3) 6 88. 3.6 933 1+ 45 + 30 3 = 3+ 3 75 = (45 + 30 ) = =1 45 30 3 3 31 3(3 + 3)(3 + 3) 12 + 6 3= = = 2+ 3(3 3)(3 + 3) 6 - 331231 = , < < 2 = , < 0. 2 2 P(x) = x 3 3x 2 + x + 2 : 1 (2, +) (x) , 139. 4.3 145 1+ 5 . (x) , 2 ,2 , x2, . , (x) . + + 1 51+ 52+2 2 x , 1 5 < x < 1 + 5 x>2.22 , . , - , : f (x) = x + 1x 1 + ...... + 1x + 0 , < f(), f() , f(x) = 0 , . : f (, f()) (,f()) xx, .yy f() (,f()) f() (,f()) Ox2 O x1 x x1 x2 x3 x f() (,f()) f() (,f()) 140. 146 4: - x 3 3x + 1 = -0 1 2. . B(2,3)3 f (x) = x 3x + 1 f (1) =1 < 01 1,51o : 2 f (2)= 3 > 0 A(1,1), , (1,2)2o : 1,1, 1,2,... 1,9 :f (1,5) 0,13 < 0f (1, 6) 0,30 > 0 (1,5 , 1,6).3o : (1,5 , 1,6) : f (1,53) 0, 01 < 0 f (1,54) 0, 03 > 0 (1,53 , 1,54) 1,53 < < 1,54. = 1,5. 1. .i) 5x 4 = 6x 2 ii) x 3 + 2x 2 9x 18 = 0 iii) 3x 5 + 5x 4 = 3x 3 + 5x 2 iv) x 6 64 = 03 2v) x + x 2 =0 vi) x 3 7x + 6 =0 vii) (x + 1)3 + 1 = 0 viii) 7(3x + 2)2 (1 x)2 (3x + 2)(1 x)3 = 0 ix) x 3 += 7(x 2 + 5x + 6) + 9x 2 36 8 x) x 4 3x 3 + 6x 4 =0 141. 4.3 1472. i) x 3 3x 2 + x + 2 =ii) 3x 3 + 8x 2 15x + 4 = 0 0iii) x 3 10x 12 = 0 iv) x 3 + 2x 2 + 7x + 6 =03. . i) x 4 + 3x 2 = 0ii) 2x 4 3x 3 + 6x 2 24x + 5 =04. , x. i) P(x) = (2 3x)(x 2 x 2)(x 2 x + 1) ii) Q(x) = + 4)(x 2 3x + 2)(x 2 + x + 1)( x 25. : i) 2x 5 162x 0ii) (x 3 x 2 + 2x 2)(x 2 9) > 0iii) 2x 3 5x 2 6x + 9 > 0 iv) x 3 4x 2 3x + 18 06. : i) x 3 + 2x 2 + 3x + 6 > 0 ii) x 4 6x 3 + 22x 2 30x + 13 0iii) x 3 3x + 2 < 0 iv) x 4 x 3 + x 2 3x 6 07. xx : i) f (x) = 3x 3 3x 2 5x 2 ii) g(x) = 4x 3 3x 18. , - f (x) =x 4 5x 3 + 3x 2 + x xx.9. :i) x 8 15x 4 16 = 0 ii) (x 1)6 9(x 1)3 + 8 =0 2 x x iii) 6 + 56 =0 x +1 x +1 10. x 3 + 5x 3 = (0,1) 0 . 142. 148 4: - 1. : 1 3 1 2 145 225 i) x + x + x = ii) x 3 x 2 x + =0, 0102 5 5632 2. , P(x) x 4 + x 3 + x 2 16x 12 = x+1 x 2. (x) = 0. 3. k , x 3 x 2 + kx + 3 = .0 * 4. x + 2x 2 = N, 2, * , 0, . 5. P(x) =x 6 5x 4 10x 2 + k k x 1 (x). k (x) = 0. xx 6. 33 5dm 9dm, . , - dm 21dm3. 7. t 3t 2 + t c = 3. , t + 50 3t 4 + 2t 3 300t 200 = 0. t . 8. 36m3, 1m x. xm xmxm 143. 4.3 1499. . V, 500=V(2000 100 + 20 2 3 ), 3 .10. t , mm - = 15t(t 2 6t 9). - d ;11. , , x 3 3 x 108cm ( ). , 11664 cm3. 3 y12. i) (1,2) 1 1B( , ). 2 2ii) y=x3+x2 x - . x 3 + x 2 5x + 3 =0iii) . 144. 150 4: - 13. . xcm : ) 200ml ,x+2 cmx+1 cm 1cm, . x 3 + 3x 2 + 2x 200 = x 0. mm. ) - 1lit, 10cm . r+10 cm r 3 + 10r 2 318 = r 0 1000r cm mm. ( 318 ). ) - , 250ml, 5cm . 5cm h+ h ( -h+5cm ).4.4 , , . .2 11o x 2 + 0 =2x 1 x(2x 1)1 x x 0 x . :2 145. 4.4 151 2 12 1x2 + = x(2x 1)x 2 + x(2x 1) 0 x(2x 1) 0 = 2x 1 x(2x 1) 2x 1 x(2x 1) 2x 4 x 3 + 2x 1 =0 x 3 (2x 1) + 2x 1 =0 (2x 1)(x 3 + 1) = 0 1 1. - 2 x = 1.2 x= x 2. x 0. -, x = x 2 4x + 4, x 2 5x + 4 =0 x1 = 4 x2 = 1. x, - x 0 . , : x = 4 : 4= 4 2 x = 1 : 1 = 1 2 . x=4. , , . - - .3o 2x + 7 x =2. x x 7 . x : 2 2x + 7 = x + 2 ( ) ( 2x + 7 ) 2 = + 2) 2 (x( ) 2x + 7 = x 2 + 4x + 4 x 2 + 2x 3 =0 3 1. - x=1 . 146. 152 4: - 4 2x + 6 x + 4 =1. x , 2x + 6 0 x + 4 0, x 3. x : 2x + 6 =1 + x + 4( )( 2x + 6) 2 = + x + 4) 2 (1( )2x + 6 =1 + 2 x + 4 + x + 4x += 2 x + 4 1(x + 1) 2 = 4(x + 4) ( )x 2 2x 15 =0 3 5. x = 5 . 2, 3 4, x , . (x) B(x) > 0 (< 0) .: A(x) A(x)> 0 A(x) B(x) > 0 < 0 A(x) B(x) < 0, B(x) B(x), A(x) B(x) > 0 A(x) B(x) < 0 (x). , (x 1)(2x 2 + x + 1)> 0. x2 + x 6 (x 1)(x 2 + x 6)(2x 2 + x + 1) > 0 , P(x)> 0 , , P(x) - x (3,1) (2, +). 147. 4.4 153 A(x) 0 -B(x) x A(x) B(x) 0 B(x) 0. x 2 4x + 3 0. : x 2 + 3x 4x 2 4x + 3 4) 0 x 2 + 3x 4 0. 0 (x 2 4x + 3)(x 2 + 3xx 2 + 3x 4 x 2 4x + 3 1 3 , x 2 + 3x 4 1 4 . : P(x) = (x 2 4x + 3)(x 2 + 3x 4) x--413 + x - 4x + 3 2+ + 0 -0 + x2 + 3x-4+ 0 - 0 ++P(x)+ 0 - 0 -0 + x (, 4) [3, +). 1. :3x 2 1 2 x 2 3x + 2x224 i) 2 =ii) =2 x 1 x xx x 1 x +1 x 1 32 2. : 2 x + x + 2x 2 = 0 3. : i) x 3 = 4xii) 3x 2 =4 iii)5x 1 = 4 iv) x + 3 = x +1 v)x +3= 10 x + 1 vi)x + x 20 = 10x 8 vii) =x+ 3 viii) 1 + 2 x = x + 12 x 4. :x2 2x + 1 x2 x 2 i) >0ii)0iii)0 x +1x 3 x2 + x 2 148. 154 4: - 5. :2x + 3 x2x 2 3x 10 i) >4 ii) 4iii) +20 x 13x + 5 x 1x2x 3 iv) v) 3x 5 x 12x 1 x + 22 1 6. : x 2 +2x 1 x(2x 1) B 1. : i) 2x + 3 < 1 3x ii) x 3 > x 5 2. : i) x + 3 x 10 =0 ii) 3x2 + 3 x 6 =0 3. : i) x 2 + x 4=x 2 + x 2 ii) x 1 + x 4= x+4 4. : i) x 1 = ii) 4x 2 + = 2x 1 5. 2 4 x 33 x 3 2 x 3x + 4 = 0 ( ) 1. (x 2 + x + 1)(x 1) = x 3 1, - P(x) = 3 + x 3+1 + x 3+ 2 x2+x+1 (,x, ). 2. :i) f (x) = x +1 ( + 1)x + 1 (x 1) 2 . - . ii) g(x) = (n - 2)x n -nx n-1 + nx -n + 2 (x 1)3 . 3. : i) x 4 + 2x 3 + 2x + 1 = 0 ii) x 4 + x 3 4x 2 + x + 1 =0 ( x 4 + x 3 + x 2 + x + = 0, 0. ). 149. 4.4 155 : x2 1 x +y.=x4. i) x 4 + x 3 16x 2 2x + 4 =0ii) x 4 + 8x 3 + 13x 2 8x + 1 =0 5. (x 2 + 2x 1) 2 3(x 2 + 2x + 3) + 14 =0 : x 2 + 2x 1 =y. 6. , x 5 + 3x 2 + x + , - x 2 2, 5x+8. 7. P(x) =17 12x16 + 12x15 12x14 + ... + 12x 1, x (11) (13). 8. - . - C , x 10x 3 100x 2 + 270x 180.= i) ; ii) ; 150. 156 4: - 2 = 1, 414213, 2,2 , = 2. 2 151. 157 2 4x1,2 =2x 3 + x = (*) 3 2 32 x= + + + 3 + 32 2 2 22 2 * 3 : x 3 + x 2 + x + = 0 - x= y x 3 + Ax = B.3 152. 158 4: - 153. 5 4 - 5.1 . : , : , .... >1 , *= , =1 :3 1 1 1 1 1 = = 2 2 2 2 8 : 1 1 0 = =1= , 0 * - . : 2 2 2 39 = = 3 241 1 2 2 , 5 4 , 0, . . O , . T - 2 .. 35 ; Av ( p )q = pq , :22 5(3 = 3= 325 5 ) 5 154. 5.1 161 2 3 x 5 = 32 , 5 32 . 52 3 5 = 5 32 .Av >0, , : = , , , , 0 = 0.2 ..83 =382= 3= 464431 11 27 =327 4= 3 == 427 4 3 27 4 3 , - .To . ..1 11 1 7+4 3 = 4 3 = 43 = 12 = 12 7 - : y 21,42x 1.4 =y 1,43,4211.4 x 3.21 +/ =7y53 5x ( 7 3 )= : x x , - ; 3 2 ; ( B . 104) 2 , , . 1,1,4,1,41, 1,414, 1,4142, 1,41421, 1,414213,.... (1) 155. 162 5: 2 3:31,31,4,31,41,31,414,31,4142,31,41421,31,414213, (2) : 31 = 3 31,4 4, 6555367 31,41 4, 7069650 31,414 4, 7276950 31,4142 4, 7287339 31,41421 4, 7287839 31,414213 4, 7288015Av : (1) , (2) , . - 3 2 . - 3 2 4, 7288. :Av >0, x x , + , ( ) , ( ).To x x. : x lim = , x>0, 0x=0.O : 332 xy 2x= 2 2xy exp = 156. 5.1 163 , , - .: , x, x1 , x 2 , : x1 x 2 = x1 + x 2 x1 : x 2 = x1 x 2( x1 ) x 2 =2 x1x x( ) x = x x( )x = x . x x . x x, : f : f (x) = x , , 1, . = 1, f(x) = 1. f(x) = 2x . : x-5 -4-3 -2-1012 34 5 111 1 1 y=2x 124 8 16 3232 168 4 2 (x, y) -y y=2x . , - f (x) = x >1,1x :0 1 157. 164 5: .y (0, +) x2 . . x1 , x 2 : x1y=x , >1 x1 < x 2 , x < x12A(0,1) x yy (0,1) -x1 x2 x. x1 g(x) = . 2 :x-5 -4 -3-2-1 01 23 4 5 x 1 1 111 1 32 16 8 4 21 2 2 48 1632 (x, y) - y . , -y=( 1 )x 2f (x) = x 0 32 9 x 2 3x > 2 3 > 12 x 3x + 2 > 0 < 1x x>2 1 2 11 2 1ii) ( )x +x < ( )x +x < ( )2 2 42 2 1 x2 + x > 2 0 < 2 x > 1x4o :i) f (x) 2x + 3 ii) g(x) = 2x 3 iii) h(x) 2x 3 + 2= =i) f -y (x) = 2x 3 .y=2 x+3 ii) g (x) = 2x 3 x . 4y=2iii) h (x) = 2x3 3 1x 2 .O 1yy y=2 x y=2 x y=2x3+2 A(3,3) 2 3 y=2x31 3 x1 x O 1O 1 161. 168 5: e . - 1 , 100% 1, 2, 3, ... , , . -: = 0 (1 + ) , =.100 =1, =1 1= 1(1 + 1)1= 2 .21 1 =2, = 2= 11 + = 2, 25 .2 2 31 1 =3, = 3= 11 + = 2, 44 .3 3............................................................................................................................1 1 1 =, = = 11 + = 1 + . : 1 2 412 52( ) ( ) ( )( ) ( ) 11 + 22,252,441406 2,613035 2,704813 1000 10000 100000 10000002,716923 2,7181452,7182682,718280 1 , , 1 + . - e. , Leohard Euler (1707-1783). e e = 2,71828. 1 = lim 1 + e 162. 5.1 169 . , , . -y e. - f(x) = ex. -y=e x .1xO 1 e Q(t) Q0 ec t = (1) , t. To Qo - Q ( t = 0) Q0 > 0, c . - . c > 0 Q , c 7 x +1 iii) ( ) x +1 < ( ) 2x 422 5. : 82x +1 32 44y 1 =3x + 2 y = 11 i) x y ii) x 5 5 = 52y +13 2 =y7 164. 5.1 171 6. :e x : e y = 12x 2 y = 8 i) xyii) e e =e2x 2 + 2 = y 6 7. w 2 101w + 100 < 0 102x 101 10 x + 100 < 0. 1. , -x 2 : f (x) = . : 2 1 i) ii) 2. :45 7 i) 4 x 1 5 4 x 2 + 1 = 0 x+2 + x ii) 3x + 3x 1 = 3 3 iii) 21 3 + 5 = 3 + 5 iv) 3 + 9 =11 4 + 4 x +1 x x +3 x+4 x+2 2xx x 1 1 1xx+ v) 4 x 32 =32 22x 1 3. 3y 2 x =1 2 x 5y = 250 i) yx ii) y x3 + 16 2 = 11 2 5 = 40 4. :x xi) f (x) = 3 ii) f (x) = 31 x1 x 5. f (x) =( + x ) g(x)= ( x ), 22 [f (x)]2 [g(x)]2 =1 6. , - 20% . i) t . ii) iii) 40 . 165. 172 5: 7. 1600 . 5 , i) , t t Q(t) = 5(0,5)1600 ii) 600 2 .iii) 20000 0,001 . 8. 40.000 15% 6 .i) 6 . ii) - . 9. x , , - x, I(x) I0 e 0,5x (x 0), = I . i) e-0,5x x = 0, 1 , 2 , 3 , 4 , 5 .ii) x, , I(x) I0 () 1 () 0,1. iii) . 10. T(t) ( C) , - 0 , T(t) T0 (1 + e 2t ) (t 0) = i) e-2t t = 0,1, 2, 3 ii) t, , T(t) T0 ( ) 1,1 () 2. 166. 5.2 173 11. C ( F) q0 ( Cb). - R ( ohm), . t q 0 eq(t) =RC (t ) i) c Rq t.ii) t kRC (k ) : 1 1 ) q 0 )q0 210 5.2 1,7%. 1987 5 . , ; = 1 (1 +) (. 100 ) t :N(t) =109 1, 017 t 5 t N(t) = 2 5 109 , 5 109 1, 017 t = 2 5 109 : 1, 017 t = 2 (1) , - y y=1,017 t , - f(t) = 1,017t2 . t 41. -1 41 x 1987, 2028.O10 2040 40 167. 174 5: , , : x = , > 0 1 > 0 , f(x) = x . - log ., > 0 1 > 0, : a x = q x = loga q :O log o : log 2 8 = 3 , 8 = 23 1log 4 2 = , 2=4 2 log10 0, 001 = 3 , 0, 001 = 103 log 0,5 0, 25 = 2, 0, 25 = 0,52 , > 0 1 , x > 0 : log = log x x= , 1 = 0 = 1, : 1 = 0 log = 1 log = -, . , , , , . 168. 5.2 175 >0 1, 1 , 2 , > 0 k : 1. log (12 ) log 1 + log 2 = 2. log = log 1 log 21 2 k 3. log = k log 1. : 1 = 1 log x log 2 = 2 x (1) 1 x1 = x 2 =2 x1 x 2 = 12 , x1 + x 2 = 12 , log (12 ) x1 + x 2 = , (1), :log (12 ) log 1 + log 2=2. .3. :log = x (2) = :x kx =k , log k =kx , (2), :log k = k log 1 > 0 = , 11 log = log = log . 169. 176 5: : 1 A = log 2 256 + 2 log 2 3 log 2 18 2 : 1 A = log 2 256 + 2 log 2 3 log 2 18 22 = log 2 256 + log 2 3 log 2 18 [ 3] = log 2 16 + log 2 9 log 2 18 16 9 = log 2 18 [ 1,2]= log 2 8 log 2 23 3 == , 10. . , log log10.: log = x 10 x = , - : log 213 213log = 2.328379603 log 0,325 0.325log = 0.488116639 e - . e. - . , ln, loge.:ln = x e x = 170. 5.2 177 , - , : ln 325 325 ln = 5.783825172 ln0,37 0,37ln = 0.994252273 10 e, . , . log ,>0 , 1 , >0 : log = log * log = x. = x , : xlog= log = x log= log log ( x log ) = :log log log= log , log = log :log ln log = log =log ln log log log, ln ln. : log17log 2 17 = 4.087462841=log 2 log > 0 1 > 0, , > 0 1 > 0 . 171. 178 5: 1 Richter R I IR = log I 0 I 0 .i) R I = 1000I 0ii) I R I 0iii) 1 Richter. Ii) 1000 0 R = log= :I0 1000I0= log= log1000 3 R= I0ii) I I (1) R = log = 10R I = I0 10R I0I0iii) I , I R, R . R= R + 1 (1) :I I 10R 10R +1 = 0 = = 10, I= 10 I I I0 10R 10R I 10 I - 1 Richter.2 p - . pH = log[H + ] , [H + ] H + .i) pH : : [H + ] - 6, 3 103 ~ : [H + ] - 5,0 109 ~ii) [H + ] : ~ : pH- 4, 2~ : pH - 6,6 172. 5.2 179i) pH log(6,3 103 ) 2, 2 pH log(5, 0 109 ) 8,3ii) pH 4, 2 , 4, 2 = + ] log[H + ] = [H + ] = [H + ] =105 log[H 4, 2104,2 6,3 pH 6, 6 , 6, 6 = + ] log[H + ] = [H + ] = [H + ] =107 log[H 6, 6106,6 2,5 3o 32 N(t) N 0 e 0,0495t , t , -= 32. N0 t , N(t) = . : 2N1N 0 e 0,0495t =0 e 0,0495t =22 1 0, 0495t =ln 2 0, 0495t = 0, 69314718 t = 14 1. , , : i) log10 0, 001 ii) log 1 10 iii) log 1 3210 2 278 iv) log 9v) log 2 16 vi) log 3 3 2 27 2. x : 12 i) log10 x = 3 ii) log 4 x = iii) log x= 2 23 3. : 3 i) log 16 = 4 ii) log 8 = iii) log 0,1 = 3 2 4. : i) log 2 3 + 2 log 2 4 log 2 12 = 10 2 + log10 5 log10 4 =2 ii) 3log 11 1 1 iii) log10 25 + log10 8 log10 32 = 21 log10iv) 2log 2 6 2log 2 3=22 3 5 173. 180 5: v) 2 log 2 (2 + 2) + log 2 (6 4 2) =2 5. t Q(t) = Q0 e0,34t , Q0 . ; 6. , p ( Pascals), h ( ) p 101300 e kh = i) k, 3050m 68900 Pascals. ii) 1000m; 7. () - . L0 6. L m : Lm = 2,5 log 6 L0 i) m L 5 100 L0 . = ii) 1 6 ; 8. S(t) ( ) t = 100(1 e kt ). S(t) i) k, 15000. ii) 5 ; 1. :111 log 2 3log3 18 1 i) 4 2 ii) 9 2 2. 1, 2, 3, ... , log1, log2, log3, ... . 3. log2 log8. - . 2 = log 2 log log 10 10 ....10 10 = 10 4. : 174. 5.3 181 5. :1 1 11 log(1 ) + log(1 ) + log(1 ) + .... + log(1 ) = log2 3 4 * 6. x> 0 : log x = log 2 x 2 *7. : i) log log =1 ii) log 2 log 3 =6 iii) log log log =1 *8. : i) log + log 1 = 0 ii) log () + log (= log () log ()) 5.3 . 4.2, x>0 log x. , x (0, +) log x, f : (0, +) f (x) = log x . , , f (x) = log x. log x = y y = x, (,) y = log x, (,) y = x . , , (,) (,) - xOy x Oy .: log x y = x y= xOy x Oy . 175. 182 5: y y y= x (,)(,) y=x 1 1y= x (,) (,) 1 x 1x >1 y=logx y=logxy=x01 :( log x < 0, 01) xx (1,0) Oy. 0 < < 1, yg(x) = log x : (0, +) y=log x, 0 0, 01 : 2log 0,5 > 1 log 0,5log 0,52 > log 0,5log 0, 25 > log 0,50, 25 > 0,5, . . 2>1 log0,5 0 x 1 > 0. : log 2 (x 2 x) log 2 2 + log 2 (x 1) log 2 (x 2 x) log 2 [2(x 1)]= = x 2 x= 2(x 1) 1 x = 2 x= x x=2 . - , x = 2. 1. : f (x) = log 2 x g(x) = log 1 x2 ; .2. : f (x) = log x , g(x) log x 1 h(x) log(x 1)==3. f (x) = x g(x) = log x :i) (2,4)ii) B(2, 4) iii) (2, 4) i) (2, 4)4. ASA DIN. x ASA y DIN y = 1+101ogx, x= 50, 100, 200, 400, 800, 1600 ASA. ; ( log2 = 0,3). 178. 5.3 185 5. : i) log(x + 1) + log(x 1) = 2 ii) log(x 1) + log x =1 log 5log22 iii) log x = (log x) iv) log(x 2 + 1) log x = 2 log 6. : i) 5x = 21 x ii) 3x 1 = 2 x +1 7. : i) log 3 2 log 3 5 ii) log 0,3 5 log 0,3 7 iii) log(x 2 + 1) log 2x 8. [H + ] > 107 [H + ] < 107. p. 1. : 1 i) f (x) = ln x ii) f (x) = ln x 2 iii) f (x) = ln x iv) f (x) log(10x 20) = 2 2. :1 x i) f (x) = ln(x + x 2 + 1) ii) f (x) = ln1+ x 3. x log178, log 81(2 x + 2 3x ), x log 3 ; 1 * 4. log= log log = = 5. : i) log x = log x ii) ln 4 x 5ln 2 x + 4 =0 6. x log5 = 5log x 2log x 5 = 5 + 4 x log5 7. :log(xy) = 4 log 2 xy = 8 y = 2x i) ii) iii) log y = 2 log x 2 log y log x + log 2 =2log x log y = 2) 3(log 8. : i) log x 2 > (log x) 2 ii) log(x 2 4) < log 3x iii) x log x > 10 * 9. log 2 3 > log 6 9 10. , > 0 : > 179. 186 5: () 1. :2 i) (x 2 3x + 1)3x 5 =1 ii) x x +3x +1 = x 2. : log + log 2 log log ( + , 1 )+ = + log 3. ( ) = 2 , log , log log (0 < , , 1, > 0) . 4. , , , : log log log 0 < , , , 1= log log log 5. log 5 = 1 log 2 x log(2x ) = 5 6. (0, ) : 2 log x 2 + log x 2 + log x 2 log x 2 = 0 7. (0, ) : (x)x = (x)x 2 8. : 27 x + 12 x 2 8x > 0 180. 187 4096 :128 32 == 5)(12 7 3 = 4096 = 12)16 (4 3 = 8= 3)44096 (12 : 4* 181. 188 5: 0 = 100.000.000 +1 = + 10.000 1 +1 = 1 + 4 , 10 1 = 1+ = 1, 00011041 8 = 0 = 10 1 + 4 , 10 0 =100.000.000 0 = 0 1 =100.010.00010 = 1 2 =100.020.001 20 = .....................................................................................................2 1 = 108 1 + 4 10 = 10 999.999.779 23027 = 230.270 = 23027 182. 189 2 4 8 16 32 64 = = = = == .... 1 2 4 8 16 32 183. 190 5: 8 1 = 10 1 + 4 10 10 104 1 1 4 4 410 10 105 10 105 1 1 + = =4 =4 1 + 1 +108 104 10 10 x= y=108105 y 4 101 = 1 + 4 x 10 1041 1 + 4 2, 718145927= 10 x = ey , y = ln x. 103 ln(1, 00984768) 9, 7995075 = 0, 0097995075 0, 0098= 184. 191y1 y= , y= 1xx Hx 185. 192 5: A = log E 186. ( ) 193 ( ) 1. : 2 x 2 3xx 2 x = 3 2. i) x + x = 2 + 2 2 .ii) (1 + t) x + t x = 2 - t (, ). 3 3 3. 3 = 1 32 , x 3 3x 2 3x + 1 =0. 12 4. ( 9) 198 22 9 9. 1+9+8 = 18 = 9. 17397 1933 9 1+7+3+9+7 = 27 -= 9. : 9, +++ - 9. : >= 103 + 102 + 10 + . - f (x) = x 3 + x 2 + x + f (x) = (x 1)(x) + f (1) x=1 x=10. 5. ( ). . : x + 1x 1 + .... + 1x + 0 = 0 . 0 - , 0 . : i) : 2x 3 + x 2 + x 1 = 06x 4 + 29x 3 + 27x 2 + 9x + 1 =0 ii) 2 12 . 6. 3x + 4 x = . 5x 7. x 2 4 2x + = 3 3 187. 194 ( ) 8. 2 log(x + 3) = log(x) ; 9. x + log x = 2 (0,) - .4 10. : log 3 (16x 2 12x ) 2x + 1 11. i) f (x) = ln x g(x) = 1 x ln x 1 x. ii) f (x) = ln x g(x) =x 2 + 1 ln x x + 1.2 12. , , , , : , , > 0, ++ = = = : 2 = 2 + 2 2 2 = 2 + 2 2 B 2 = 2 + 2 2 13. , , , , : , , > 0, ++ = = = () = , (KM) = , () = , = , = , = 14. , , , , : 2 = 2 + 2 2 0 < , , < 2 = 2 + 2 2 2 = 2 + 2 2 : = = ++ = . 15. , , , , : 2 = 2 + 2 2 0 < , , < 2 = 2 + 2 2 2 = 2 + 2 2 , (M) = , (KM) = , () = , = A, = , = . 188. - 195 - 3 5ii)(3, 1) (21, 24) , . 4 3 (3, 4) (5, 2). 3, = 3, +2 3 ,, 2 = 3,(2, 1).10. x = , y = , z = . ( 3 + 1)( + 1), , )11.(4,3, 5)f (x) = x 2 4x + 3,(10 + 2, 16 + 2, ), g(x) =x 2 + 2x + 3,1h(x) 0,5x 2 3x + 4.= 1 : y = x + 2, 2 : y = 1 x2 (1, 2), (2, 1).111R= T + . 600 302 42. , 3 311 3 2 3 2 1 = , 2 =22 3 2 , 2 , . 2 1, 3 2 3 2 , 22 2 + + 1 ,, (1, 2), (1, 2), (2, 1), (2,1). +1 +1 189. 196 - (4,3), (4,3), (0, 5).(1, 0), (3, 0), (2, 1), (4,3).1. x = 3, y = 3 2, = 450. 2. = 1, = 3.3. 2 1. (,1],[1, +), (, 0],4.63 [2, +),(, 1], 33 [1, 0], [1, +). 4f (1) = 1 5460 18000h(1) = 2, h(1) = 2 . f (x) f (3) 1 3 36. , ,, 3g(x) g(1) 2 2 33 13 , , 3, 2 220, 1, 0, 0,1, 0, 478, 733, 1062 58. 2 22 2. 4. f (x) =2 (x 1) 2 + 32f (x) =2 (x 2) 2 1. 12 + 8 3, 12 32(x 2) 2 2(x 3) 2 32(x + 2) 2 2(x + 3) 2 3 190. 197 3. + ( + ) =180 , ++90. =43 42 2 x = , x = , x = .54 35 52 52. x = , x = , x =. 3 25 1 33. x = 3, x = , x = . 225 524. x= , x =, x=. 2 3 35. 8 5 20 . 5 2.6. 2. 2 122 2 2 1 2 1 x(3 2 ) y = x, y = , y = 3x.22 y = x, y = 3x, = 0,5x, y 3.3 y = 2,5x.3 1 3 1200 =, 1200 = , 22 2 23 33 1200 = 1200 = . 3, 3 13 ii) (2850 ) = 2 , (2850 ) = , 23 (2850 ) = , (2850 ) = 3. 3 x = , 187 1= , 187 3 3 = x= 2 + x= 2 +, 62 6 24 2187 3187 =, = 3. x = + , 6 3 6 2 21= 2 , 21 = 2x= 2 , 42 42 472121x= 2 x= 2 +, = 1. =6 6 44 191. 198 - 22 , .x = + 45x= 2 , 6 + 6 + 22=x = x , 3 99x= 2 , 6 + 2 4 =x , 9x= 2 + , .x= 10 + 5, x = , 42 + 7 x = + , = x , 612 x = + , 5 4 x=2 , 6x = + , . 624 + 7 24 x = , 624 = x, x = , 36 312 =x , .x= 2 +x= 2 +60 23210. =2 x= 2 + , 2 3 5 = 2 +x= 2 x= 2 +644 x= 2 , 55 == 2 , , 2 66x = x = + , 34 x= 2 , 2 3x = 2 x = 3 3t = , . 6 x = + , 2 223 x= 2 x= 2 , x= 2 +x= 2 + , 33 5 5 2 x= 2 , 33x= 2 + , 5412.x= 2 , 5 3. 192. 199 3x1xx= ,g = 7 2 22x3 x= 2(1 + 3) 2 7. 105 =, 3 4g = 7. 2 2(1 3) 105 = , 4 105 = 2 3, 105 = 2 + 3, x = , 2(1 3) 8 195 =, 4 =x + , 5 30 2(1 + 3) 195 = ,x = + , 4 4 2 195= 2 3,x = x = +, 4 5 195= 2 + 3. 2x = +, 335 ( + ) = ,13 65.564( + ) = , 65 , .332( + ) = , 56 7 13 19, ,, 5612212 12 ( + ) =.33x = + , 6x = , 11 3 22 x = + , 42 x 2 ( ) = 3 193. 200 - ( + 2) = (( + ) + ) = .... 2 2+ 2= , 5 162+ 2+ 2 3. x =x=. 4 4 2+ 2+ 2 4. = ,= .4162 2+ 2 4 9 = = .... =, =, 4 2 13213 2 2 3 8. x =x=.= , = . 6 3 2 32 2 14 = , = ,2 525 1 = , = 2.32221 2 2 3 x= 2 x= 2 , 233 x= 2 , 4 23 6x= 2 , 2 247 x= 2 + , 2 =, 2 =, 25 25 2472 =, 2 = . 724 3 3.+ =,8 8 2163 ( + 2) = = ...13 8 8x= 2 x= 2 + , 6. x= 2 x= 2 + x= 2 + 5 , 2 26 6x= 2 x= 2 + , 3 2x = + x = , 3 3 2 2+ 2 = ,1622+ 2+ 2 13+2 =, , 16 24 4 194. 201 11 44 3x x++ = 2x 6x 2x + 8x 1 (8x 4x) 2 1 2x 2 11 2 + f (x) = 2 x +x = = x, 6 3 10 3 2 + 2 f (x)= 2 x + =x =x , 4 82 4 f (x) = 2 x + 62 3 22 5. 23xx 2 4xxf (x) = 2 x 4 2 2x 2x x4 2 2 + x= 2 , 4 2 3 x 2 2.x= 2 22 x= 2 , x = x = 2 + 46 5 x= 2 + , 7 6x= 2 12 711 x = x = + x= 2 + , 121212 =x, 35 6 + 2= = x= x=12126 9 6 2=x , 2. () + () 2 2 + = 94= ,4() + () = 2 2. 195. 202 - 3. 10 x= 2 +6 2 2 + 2, 2 2 + 2. 5 x= 2 + , 76 4. x = + x = +, 2424 136. 3 5. = , 47 (10 + 2 2)m,= 40( 2 1)h (10 2 2)m 6.= , (t + 1) 810 + 4 4 P= 1+ 2 6 2 2 6+ 29., , 42 412. x= 2 + 1. AB 284 m4 2. B 1,58 m 2 = x + , 5. 11503 4 6. 51, 2 m13. = 200 2 2 + + 200 S4 7. 60, 25 = = 200( 2 + 1), Smax8 1.-5.15. B = 60 , =45 6.-7. 8.-10. 1= 1. 2 11. = 300. 2. 1 3. = 2 3. 4. =1 4. x= 2 , 5. 1 1, 3 196. 2035. P(11) =48406.7. P(x) x y =1. = 10, P( y) = 02. = 2, = 198.3. = 3, = 59.P(x) x + 1=P(1) =0.4.10.2 2 0, , 3 322= =331.x x =5. P(x) = x 2 5x + 1. 2.P(x) = (x + )(x) + = 0 = = 3. x 1x2 21.(x) = 3x 3x 8, 4. P(0) = 0, P(1) =0, 3 2 1(x) = x + 3x + 9x + 27, P( ) =0 2165 5. = , = 1 (x) = 4x 3 , (x) = 632 (x) = 2x + 1, (x) = + 3, (x) = 6x 2 8x + 3 x66 (x) = (x) = x 2 + 7x2 ,1.0,, 2,3, 3552.53. k = 40,1, 1, 2, 234. (x) = x 2 + 10x 25, = 01, 2, 3 2 (x) x 2 8x + 64, 0==213 ,1, (x) x 4 + x 3 + x 2 + x + 1, 2==322(x) = 3x 3 6x 2 12x 24, = 482,9 + 4 5,9 4 5(x) 4x 2 + 14x 30, = 0= 2, 2 , 1, 2 197. 204 - 2.1, 4 21 3. 1, 2 1, 5 1. x = 3 2, 2 6.x > 2x =1 x < 2 2. x = 2 + x = (2 + 1) , x 1 x2 66 13. 7. ( , 0) 2 591 8. 2 5 < x < 0 1 < x < 2 + 5 36. x 1x>0 9.2, 2 ,2 5 321.x< 25 1.1, 2, 43, 2, 15 x 5 < 0, 2. 1, 2, 2, 3x 5 02. 3. 3,1, 7, 11 4. 3. 3, 24. < 0, 0 5. 1, 1, 2 + 3 2 ,2+3 2 x< , x 22 6. 7. t 4, 6 c 0, 455. 2 + x= x= 2 +2 6 8. 9. x= (2 + 1) , 6 10. 11. y + 4x 108x 2 y = 11664, 1. P(x) (x 2 + x + 1) = 12.= 5x 3y x 3 1 + x 3+1 x + x 3+ 2 xx1 = 1x 2 = 32. (3, 18) f (x) =x (x 1) (x 1) = 198. 205 .... (x 1)P(x) =4 P(x) = (x 1)(x)x= x = 19g(x) (x 1)P(x) = 3.x = 1P(x) (x 1)Q(x) = Q(x) = (x 1)(x). 4.23. x 5. 1 x+ = y. x4.x21 1.