document
TRANSCRIPT
1. .162 222015 1937 .8622/2 . : 1.42.2. .4186/2013(193) . 2.2.3.. .3966/2011(118) , , . 3...89/2014(134), . 4.90 ..63/2005(98). 5..3/14012015.. . 6. , : : 2. 1938() 3. ()1939 1.2. 4. 1940() , , , , , , , . 5. ()1941 6. 1942() 7. ()1943 8. 1944() ( ) () . .. , , 1000 , . 19 . , , , . .. , . , , . ( ) , , , , . .. 0,70.1, 7,6 , (), 2030. . 40% . . 6 . (. ), ( ), . . .. . . 9. ()1945 10. 1946() 11. ()1947 . 12. 1948() 13. ()1949 0A 14. 1950() 15. ()1951 16. 1952() 1.1.1. . 1.1.2. 17. ()1953 (, , Venn). 1.1.3. ( ). 2.1. (1 ) 2.1.1. (, , Q, R-Q). 2.1.2. . 2.2. (8 ) 2.2.1. . 2.2.2. 1 . 1 . 2.2.3. ( , , ) . 18. 1954() 2.3. (5 ) 2.3.1. . . + < < < 2.3.2. 1 . 1 . 2.4. (5 ) 2.4.1. . 2.4.2. ( ). = = + + 19. ()1955 2.4.3. , . = < 2.5. (3 ) 2.5.1. - x = . 2.5.2. - . : = , = = 2.5.3. x = ( ) = = 3.1. (6 ) 3.1.1. . 3.1.2. . . 20. 1956() 3.1.3. . 3.1.4. (, ). 3.1.5. , , . . 3.1.6. . 3.2. . = + 3.2.1. = + . 3.2.2. = + . 3.2.3. = + . 21. ()1957 = 3.2.4. = = , . = . = = 3.2.5. = + + = . M = + + , . ( )= = + = + ( )= + ( ) = 4.1. 2 (5 ) 4.1.1. = + + xx + + = . 4.1.2. 2 . 4.1.3. 22. 1958() . 4.1.4. 2 . 4.1.5. 2 . 4.2. 2 (5 ) 4.2.1. = + + + + > ( + + < ). 4.2.2. 2 2 . 4.2.3. 2 . 5.1. 22 (3 ) 5.1.1. + = . . + = + = . . + = . . 5.1.2. 2x2 . = + 23. ()1959 5.1.3. 2x2 , . 5.2. 33 (1 ) 5.2.1. . 5.3. 22 (1 ) 5.3.1. , . 5.4. (2 ) 5.4.1. . 5.4.2. . 6.1. (2 ) 6.1.1. . 6.1.2. (.. , Venn, ). 6.2. (1 ) 6.2.1. , . 6.3. (3 ) 6.3.1. . 24. 1960() 6.3.2. . 6.4. (2 ) 6.4.1. Venn . 7.1. - (4 ) 7.1.1. . 7.1.2. , , . ( ) + = 7.1.3. . 25. ()1961 25 7.2. (2 ) + = = = + = 7.3. - (4 ) 26. 1962() = = i) T . ii) . 27. ()1963 iii) . 32 5 9 +C i) + ii) + + = + + + + 28. 1964() 29. ()1965 30. 1966() ( )= 31. ()1967 32. 1968() 33. ()1969 < + = = + + = 34. 1970() 35. ()1971 = + 36. 1972() 37. ()1973 38. 1974() 39. ()1975 1. (2 ) 1.1. (1 ) 1.1.1. . 40. 1976() 1.2. , , , (1 ) 1.2.1. . 2. (4 ) 2.1. (1 ) 2.1.1. , . 2.1.2. . 2.2. (3 ) 2.2.1. , , .. 2.2.2. . 2.2.3. . 2.2.4. . 3. (8 ) 41. ()1977 3.1. 5 (1 ) 3.1.1. . 3.2. - (3 ) 3.2.1. . 3.3. (3 ) 3.3.1. , . 3.3.2. -. 3.4. - (1 ) 3.4.1. . 4. (12 ) 4.1. (3 ) 4.1.1. . 42. 1978() 4.1.2. . 4.2. (2 ) 4.2.1. (, , , ) , . 4.3. , (2 ) 4.3.1. . 4.3.2. . 4.4. (2 ) 4.4.1. . 43. ()1979 4.4.2. . 4.5. , , (3 ) 4.5.1. ) 5. (18 ) 5.1. : , , (3 ) 5.1.1. . 5.1.2. . 5.2. : , , (3 ) 5.2.1. . 5.2.2. . 5.2.3. (, ) . 5.3. (5 ) 5.3.1. . 44. 1980() 5.4. : , , , (5 ) 5.4.1. . 5.5. (2 ) 5.5.1. . 45. ()1981 6. (6 ) 6.1. (3 ) 6.1.1. . 6.1.2. , , . 6.2. - (3 ) 6.2.1. : 6.2.2. : 6.2.3. : 46. 1982() 47. ()1983 48. 1984() 49. ()1985 50. 1986() 51. ()1987 0 2 x 52. 1988() 53. ()1989 54. 1990() 55. ()1991 > 56. 1992() y x y x x y 57. ()1993 = = = + = = = 58. 1994() 59. ()1995 ( ) 22 1 1 = = i is x x 60. 1996() = 61. ()1997 62. 1998() = = = = [3, )+ 63. ()1999 [ 3,0] ( , 3] (0) 0f + = = + > + = 64. 2000() = + = = = + + = + + = + + = + 65. ()2001 66. 2002() + + + = + = + = 67. ()2003 + ( ) ( ) ( ) ( ) = = = = = = ( ) ( ) ( ) = = = ( )( )+ 68. 2004() = = = = = = = = + = = + = = = 69. ()2005 = I L I L I = 0I 12 10 0I 70. 2006() 71. ()2007 72. 2008() 73. ()2009 74. 2010() 75. ()2011 76. 2012() 77. ()2013 = 78. 2014() 79. ()2015 80. 2016() 81. ()2017 82. 2018() = 83. ()2019 84. 2020() = 85. ()2021 86. 2022() 87. ()2023 88. 2024() 89. ()2025 90. 2026() 2 2 91. ()2027 92. 2028() 93. ()2029 ( ) ( ) 1 1 2 2 // det , 0, det , = = x y x y ( )1 1 ,x y ( )2 2 ,x y 94. 2030() 95. ()2031 x' x ( )0 0 0 M x , y ( )1 //= , 0 M M M ( )0 0 0 ,M x y y' y ( )0 1 //= , 0 M M M 96. 2032() + =x y 0 0 ( )0 0 0 M x , y ( ),=n + =x y 0 0 = +o o x y ( ),=n 97. ()2033 + =x y 0 0 + =x y 0 0 2 2 + = + = x y x y 0 0 0 0 ( ), ( ) , 98. 2034() ( ) ( )2 2 2 1 2 1 1 2 ... 6 + + + + + = ( )1 1 1+ + > , ( ) ( )( ) , f y f ( x ), x= 99. ()2035 1 = , ( 1) 1 = + l ( ) l = = 2 1= + ( ) + ( ) 100. 2036() + 1 0 k k lim lim , k + + = = + 1= > , lim + 1> 0 1 1 lim , lim , + + = < = + > 1 < 101. ()2037 30 /=E u m s 50 /=H u m s 102. 2038() , , , , , , , = x = y 103. ()2039 1 3 = ( ) ( ) = = 104. 2040() pF 20N= 30 // ( ) 2 2 2 // ( ) ( )( )2 2 2 2 2 1 2 1 2 1 1 2 2 + + +x x y y x y x y 1 1 2 2 x ,y ,x ,y 1 1 2 2 0 x y x y = 30= 5h m= 105. ()2041 W w x W // K y W K x' x y' y x' x 1 2 1 1 x , y 2 2 x , y 2 1 2 1 y yy x x x 1 2 = , 1 2 = y x 106. 2042() ( )0 0 0 M x , y ( )= , ( )M x, y 0 0 =r OM =r OM 0 M M 0 = + r r t , t 0 0 = + = + x x t , t y y t 0 ( )0 0 = = = = y y x x , ( )0 0 = y y x x 0 0 1= + = + x x t , t y y t ( )0 0 0 M x , y ( )1= , 107. ()2043 0= 0 =x x 0 0 0 1 = + = + x x t , t y y t ( )0 0 0 M x , y ( )0 1= , ( ) =n , ( ) = , + =x y n n n 108. 2044() ( )2 2 : 3 = x y , 109. ()2045 0 0= = = 1 2 1 2 : 3 7 : 3 3 3 = = x y x y 1 2 = =n n 1 2 = = 1 2 110. 2046() 1 2 : 6 1 3 : 5 3 1 = + = x y - x y 1 2 = =n n 1 2 = = 1 2 1 2 : 8 6 10 : 4 3 5 + = + = x y - x y 1 2 = =n n 1 2 = = 1 2 = + = + + = 111. ()2047 112. 2048() 0 9999, ... 1 2 3 40 9 0 99 0 999 0 9999= = = = . , . , . , . , ... 1 1 10 = 113. ()2049 114. 2050() 115. ()2051 ( 80) : - . y ln x y log x= = . 1. y x = + 2 y x= 3 y x= y x = y x= , . 2, 3. 116. 2052() 4. ( ) ( ),y f x y f x= = ( )=y f x 0 x 0 x 0 x 0 x + 117. ()2053 ( ) ,f x c c= ( )f x x= ( ) 2 f x x= ( )f x x= y x= y x= = x y e y ln x= 0 x 118. 2054() : =y x , =y x , , 0 1 x y = < , = y x . : http://webspace.ship.edu/msrenault/GeoGebraCalculus/ derivative_app_opt_wire.html 119. ()2055 . ( )( ) ( )=y f g x g x f ( ) ( ) ( ) f x dx G G = G f 120. 2056() 1 ( 1.2.1) ) ) ) ) 121. ()2057 ) ) ) ) 122. 2058() ) 2 ( 1.2.1, 1.2.2, 1.2.3 1.2.5) . x x 123. ()2059 x 3 ( 1.2.3) 110 . 7500 60 , . 4 ( 1.3.1) ( ) 0.5 1= +c p p , , p . t , ( ) 2 10 0,1= +p t t . 6,8 5 ( 1.3.2) ( ) 2 1f x x= 124. 2060() x ( )f x ( ) f x ( )= y f x ( )y f x= ( )= y f x ( )= y f x x ( )f x ( )f x ( )y f x= ( )=y f x ( )y f x= ( )y f x= 125. ()2061 [ . . .] [ . . .] 6 ( 1.6.2, 1.6.3) ( ) 2 2 1 1 x g x x + = g 7 ( 1.7.1, 1.7.3) , ( ) 2 1 1 = + f x x . 8 ( 1.8.1) 126. 2062() 9 ( 2.1.1, 2.1.3) ( ) 4 2 2= f x x x 0 1= x , 1 0=x 2 1=x . 10 ( 2.3.2) ( ) 2 0,5 17c p p= + , , p . t , ( ) 2 3,1 0,1= +p t t . , , 3 ; 11 ( 2.3.2): ( ) 2 20 8000= + +P x x x . 12 ( 2.3.2, 2.3.1 2.3.3): , . 1 . 4 , . 13 ( 2.3.1, 2.3.2) , ( ) t ( ) 2 0 016= + +H t t S t H , 0 H 0S . 127. ()2063 14 ( 2.3.1, 2.3.2): 0t = , 32 . : ( ) 2 16 16 32= + +s t t t , s t . 15 ( 3.3.2) , ( ) 2 = + +f x x x 2, 2 1f ( ) = 16 ( 3.3.3): q , ( ) 2 3 5 75= + +C q q q , . , ; [ : , ( )A q , , ( ) ( )C q A q q = ] 17 ( 3.4.1) : ) ( ) ( ) 1 1 f x x x = ) ( ) 0x g x xe , x = 18 ( 4.1.1, 4.1.3) 128. 2064() + , , q . 900 , 5 . [: ( )) 19 ( 4.1.1, 4.1.3) , . x , ( )10x220 , . ( ) 20 ( 4.3.1) x , , ( ), x62 + . 5000 , 9 . 21 ( 4.3.1) x ( ) 2 1 x50xR += , , ( ) x5200xR2 += , . , : 22 ( 4.2.1, 4.3.1,4.4.1) xx 2=y x 1=x 3=x 3 1 2= I xdx 23 ( 4.2.1, 4.3.1, 4.4.1) xx 4 1= y x yy 3=x 3 0 ( 4 1)= I x dx 24( 4.4.2) 1 2 ,m m , 1 2 2 = m m F G R , R G . , =R a =R b . 129. ()2065 ( ) 130. 2066() 131. ()2067 132. 2068() : , . . 133. ()2069 134. 2070() ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 135. ()2071 136. 2072() ( ) ( ) ( ) 137. ()2073 Bernoulli . 138. 2074() 139. ()2075 140. 2076() ( ) 141. ()2077 o o ( ) o 142. 2078() 143. ()2079 ( )2 2 x- - 2 1 f(x) = e 2 144. 2080() 145. ()2081 146. 2082() 147. ()2083 148. 2084() ( ) ( ) 2 2 2 S x x= , , : xi yi X Y yi=xi+ , X Y : 33. 149. ()2085 . , , . 34. 4.3.1. . 35. 4 36 . . 150. 2086() , , , . . , . . , . , . Pearson . 151. ()2087 . 5.1.1., 5.1.2 5.2.1 29. ( ) M( ). y=+x x= x y. y y=+x x (xi,yi) 152. 2088() 5.3.1., 5.3.2. 5.3.3 30 31. , . 5.3.3. 32. 153. ()2089 154. 2090() 155. ()2091 156. 2092() = 157. ()2093 158. 2094() 159. ()2095 160. 2096() 1 2 3 4 5 6 7 8 9 10 CD (x) 125 172 220 186 95 90 176 255 163 262 (y) 50 71 102 86 41 38 70 120 71 122 161. ()2097 162. 2098() 163. ()2099 . . . . , ( ), , , . , . , - , . , , , . . , , , . . , , . , , (.. ), , , . , : 1: (, , , , , ). . . , , . 2: 164. 2100() , , . , , , .. . 3: , . , . , , , , , , . , , . , , . 4: , , , . , , , , . 5: ( ) , , . , .. . , , ( ), . , , , , . , . . , , , , . , , , . . , . , , , . : : . . 165. ()2101 , . . , , , , . ( ) (.. , ), . ( 125) : - . 1. f g =f ( x ) g( x ) >f ( x ) g( x ) , ( )( )f g x > . 3.2.3. , . .. Fermat . . 15. 16. / , , ( 1 ), . . (4 ] 17. 1. (7 ) 4.1.1. . , , : i) 172. 2108() ii) {0 x , + f , 0 x g 0 x + . iii) {0 x , + f , 0 x g 0 x . . .. 4.1.3. i) y x= : 0 lim 1 x x x = , . ii) y = : 2 x x , x= . 18, : 1. . 2. f 0 x , 0 x , .