Математический анализ и линейная алгебра. Учебно-методическое пособие (29-10)

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, .. 2010 22.3, .. : .. , .... .. , .. , .. , .. (. ); . ... (. ); .. (. ); .. , .. (. ); .. (. ); .. (. ); .. (. ); .. (. ); .. (. ); . . .. , .. (. ). . , .. , , .. . , / .. .. . .: , 2010. , , , , , , . 22.3(),20103 (, , , , ) . , , , . , , , . : 1) ; 2) ; 3) , . , , . .4 : , , . , . , 1 2, . .511.:/... . .: , 2010.2.:/... . .: , 2010.3. : / . .. . I, II. .: , 2010.4. . . .: , 2007.5. . . .: , 2009.1. .., .., .. : : / . .. . .: , 2009.2. .. : . .: , 2006.3. .., .. : . .: , 2005.4. .., .., .. : . 1, 2. .: , 2007.5. .. . : . .: , 2006.1. (1).2. ().3. LANTESTING STELLUS.4. STELLUS.5. .1 ( ) [1] [2] [3]. .6 . , ( ) . ( ) , . (. . 1220 ). 1. , , . 2. , ( ). ( ). ( 1 , 2 ). , 7 . ( ) ( ) () ( . [5]). ( ) ( . [4]). , . , , . . 1 , (), . , , , , , . . . . . ( ). , , , . : 8, , , , , . , , , . , , . . . , , . . , . , . , , , ( ( , , .) ) . , (, ) (, , ) . , , . . ( , ), (, ) . , , , () . , , . , , , . , . 9 . () ( ), ( ). = | | . a , , . , | x a | . x:xAo =. , | |, , aAo =. , 100aAo = (%). , = | | . . 0 , . . , , . , 10 , , (n + 1) . . , . , , , . . , , , ; , . 5, , . , ( ).. = 3,1415926... , 3,14 ( 1 0, > 0. , , . , 1 ([1, 6.5] [3, 6.5]), , . ( ) : 1lim 1xxex| |+ = |\ . ( )1/0lim 1 .yyy e+ = ( , ) , , , ( ). , , . , .19 III. 6. , . , , . . . ( ). . . [1, 7.17.7], [2, 7.17.3] [3, 7.17.7, 7.11,7.12]. , : . . , ([1, 7.6] [3, 7.10]), y = f (x) . , . , . , , ([1, 7.2] [3, 7.2])., , , , , . ([1, 7.5] [3, 7.5]) . , , ([1, 7.4] [3, 7.4]). . 20, . . 7. ( ). . . . ( ). , . ( , , , x , , , ) . y = ax2 + bx + c . y = (ax + b)/(cx + d) [1, 8.18.5, 8.78.9], [2, 8.18.3, 8.5] [3, 8.18.5, 8.7, 8.8, 8.108.12, 8.14]. [0/0] | |/ ([1, 8.2] [3, 8.2]). , (8.3) , . , . , . , ([1, 8.8] [3, 8.8]. 6 , , .21 8. . . . [1, 9.1, 9.2], [2, . 9] [3, 7.77.9, 7.13]. y = f (x) ( x ) dy =f(x) dx. [1, 9.1] [3, 7.4]. , . ( ). , y = f (u) dy = f(u) du , u . . IV. 9. . . . . ( ) [1, 15.1, 15.3, 15.6, 15.9], [2, 15.115.4] [3, 9.1, 9.3, 9.7, 9.10, 9.129.15]. . , 22 . , ([1, 15.2] [3, 9.2]). , . . () , . ([1, 15.6] [3, 9.7]), . , . , , , ( ). , () . . , . , f (x) 211niin =o = o, ( )i i if x y o = , n (xi, yi). , , (x1, xn) () ().23 V. 10. . ( ). . , . [1, 10.110.5, 10.8], [2, 10.110.3, 10.5] [3, 10.110.6, 10.910.11]. , , , , , : f (x) . . . ; . . , ([1,(10.17)][3,(10.19)]), , . , . , , . , :) x t:( ), x t = ( ); dx t dt ' = 24() ( ) ( ); f x dx f t t dt '( = } }) t x:(), t x = (); dt x dx ' = () () ( ). f x x dx f t dt '( = } } , () () . , , ( ), . t x, t x , . ([1, 10.3, 10.6] [3, 10.3, 10.6]). ([1, 10.4] [3, 10.4]), , u dv. , , , , ([1, 10.1010.13], [3, 10.8, 10.9]). 11. . . . . . . . [1, 11.111.8, 11.10],[2, 11.111.4] [3, 11.111.8, 11.1111.14].25 , , , . , ([1, (11.15)] [3, (11.15)]) . . , , ([1, 11.3, 11.18] [3, 11.3,11.23]). , uv , ([1, 11.4] [3, 11.4]). , , :| ); , + ( | b ; ( | + ; . ( ), . ( ), . . , , , , , . , , , .26 . , , . ( , , ) (. .) , ( ) ( ). 12. . . . . (, , ) [1, 12.1, 12.2, 12.412.6], [2, 12.112.4] [3, 12.1, 12.2,12.412.6, 12.1112.14]. , , , ( ) . ([1, 12.3] [3, 12.3]) . , ( ), y f x y ' = , ( )0 0y x y = , , . , , ( ), f x y .27 , , . VI. 13. . . . (). . : , , . . . [1, 13.113.5], [2, 13.113.3] [3, 13.113.7]. . , 1nnu=, u1 + u2 + + un + , , () . . , . , . , , , , . , ( 0nu n ) , , lim 0,nnu= . ( ). 28 , , . , , . , :1) 11nnaq= |q| < 1, |q| 1;2) 11nn= ;3) 11nno= 1; o > 1. o s , , 1lim 1nnnuu+= . . , . , , , . .1. .2. . , . , . . , ; 3.3. , , .29 14. . ( ). , . . . ex,ln (1 + x). . : [1, 14.114.4], [2, 14.114.3] [3, 4.114.6]. , , , , . 1limnnncRc+= , n, cn+1 (n+1) , . (R; R) , , , , = 0 ([1, 14.2, 14.3, 14.3, 14.7] [3, 14.2,14.3, 14.3, 14.7]). , . , , . , , . , , , ( ), 30. , . , , ex, ln (1 + x), (1 + x)m ([1, 14.2] [3, 14.2]) . , .. ([1, 14.3] [3, 14.6]). , :) , ;) , . , , , ([1, 13.4] [3, 13.4]). 1. . . . . : , .2. 2, 3 n ( ). .3. . . . , , .4. k . (). . .5. () . .316. . (, , ). n . .7. . .8. ( ) . (). , .9. n . .10. ( = 1).11. ( ).12. . . . , ..13. . (, , , ) .14. . . ( ).15. , . .16. n x . ( ).17. . ( ).18. (). ( ). , .19. , . .3220. . , . . .21. . .22. . ( ).23. ( ).24. ( ). .25. ( ). .26. ( ).27. . ().28. ( ).29. . , . .30. . .31. . . (). .32. . ( ).33. . .34. . ( ).35. .3336. ( ). .37. . .38. . .39. . ( ).40. . .41. . . . .42. ( , ) . .43. . .44. . . (). .45. ().46. . .47. . . .48. . . = x (). .49. y = ln (1 + x) (). .50. = (1 + )n (). .34 [1], [2] [3], . ( ). ( ) (, ). , [2] [3] , .35 [1] [2] [3] 1 2 3 4 I I. 1.11.13 1.11.5, 1.241.27, 1.511.53 1.11.6, 1.81.15, 1.371.39, 1.681.70 1. 1.141.20, 1.221.29 1.61.23, 1.291.50, 1.541.65 1.161.29, 1.401.48, 1.511.57, 1.601.67, 1.711.87 3.2, 3.3, 3.7 3.24, 3.26, 3.71 3.2, 3.3, 3.373.39, 3.84 2. 3.183.20, 3.27, 3.28 3.373.42a, 3.43, 3.44, 3.743.79 3.503.55a, 3.56, 3.57, 3.873.92 2.12.3, 2.6, 2.7 2.12.4 2.12.3, 2.92.13 3. 2.11, 2.12, 2.152.18, 2.212.23 2.62.32 2.142.43 II. 4.14.3, 4.5, 4.10, 4.12 4.1, 4.4, 4.5, 4.7, 5.1, 5.4, 5.6, 5.7 4.2, 4.3, 4.5, 4.16, 4.18, 5.1, 5.2, 5.65.8, 5.12, 5.15 4. 4.144.19, 4.214.23 4.114.14, 4.234.32, 4.344.46, 5.125.16, 5.225.26, 5.36, 5.37 4.334.42, 4.474.58, 5.165.19, 5.235.31, 5.46, 5.47 6.16.3, 6.5, 6.6, 6.86.11, 6.13, 6.14 6.16.6, 6.126.17, 6.45, 6.46, 6.68, 6.69, 6.976.99, 6.168, 6.169 6.16.3, 6.5, 6.6, 6.86.11, 6.81, 6.155 5. 6.18, 6.206.27, 6.336.36, 6.386.41 6.76.9, 6.11, 6.186.23, 6.256.27, 6.306.34, 6.366.39, 6.43, 6.44, 6.476.67, 6.706.96, 6.1006.120, 6.1706.175 6.126.79, 6.1106.132, 6.1466.153, 6.1566.165 III. 7.17.8, 7.10, 7.13, 7.157.17 7.1, 7.2, 7.13, 7.15, 7.109, 7.110 7.17.8, 7.10, 7.197.22, 7.25, 7.105, 7.106 6. - 7.207.29, 7.35, 7.42, 7.43, 7.467.49 7.3, 7.57.8, 7.9, 7.10, 7.21, 7.25, 7.26, 7.287.31, 7.347.37, 7.41, 7.427.46, 7.48, 7.53, 7.54, 7.1137.115, 7.1227.127 7.267.51, 7.64, 7.65, 7.907.100, 7.1077.115, 7.1177.119 368.1 8.3, 8.48.7, 8.9, 8.118.15, 8.17 8.1, 8.9, 8.10, 8.13, 8.14, 8.35, 8.36, 8.388.40, 8.948.97 8.18.8, 8.10, 8.128.17, 8.25, 8.26, 8.288.30, 8.51, 8.52, 8.548.56, 8.1108.113 7. 8.198.34, 8.418.53 8.48.6, 8.158.22, 8.25, 8.278.30, 8.41, 8.52, 8.558.57, 8.698.71, 8.758.77, 8.1008.102, 8.105, 8.106, 8.1088.118, 8.120, 8.121, 8.123, 8.124 8.208.23, 8.318.38, 8.41, 8.438.46, 8.578.73, 8.75, 8.778.79, 8.81, 8.82, 8.848.87, 8.89, 8.918.94, 8.1168.118, 8.121, 8.122, 8.1248.134, 8.136, 8.137, 8.139, 8.140 9.1, 9.3, 9.5 9.1, 9.2, 9.6 7.127.14

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