1. Математический анализ (850924), страница 17
Текст из файла (страница 17)
,%) !)':py = x ; ln(2 + e + 2 e + e + 1):x2xx2. ,%) !)':y = (arctg x)3. ,%) ) dy:(ln arctg x)=2:py = x arcsin(1=x) + ln jx + x ; 1j (x > 0):24. C % % :y = 4x ;4 x x = 2:020! 21. ,%) !)':y = e8 (2 ; sin 2x ; cos 2x):2x2. ,%) !)':pp:y = (sin x)3. ,%) ) dy:py = tg(2 arccos 1 ; 2x ) (x > 0):ln sinx24. C % % :0y = 2x + 3x ; 1 x = ;2:20289! 31. ,%) !)':y = 12 arctg e 2; 3 :2. ,%) !)':xy = (sin x) x :3.
,%) ) dy:ppy = 1 + 2x ; ln(x + 1 + 2x) (x > 0):5e4. C % % :0y = x ; x x = ;1:30! 41. ,%) !)':2:y = ln14 ln 11 +;22. ,%) !)':xxy = (arcsin x) x :3. ,%) ) dy:ppy = x arctg x ; 1 ; x ; 1:e2224. C % % :0y = x + 8px ; 32 x = 4:20290! 51. ,%) !)':p1 ; 1:y = 2 e + 1 + ln pee ++1+1pxxx2. ,%) !)':y = (ln x) x :3. ,%) ) dy:3y = arccos p1 +1 2x (x > 0):24. C % % :0py = x + x x = 1:30! 61. ,%) !)':y = 32 (arctg e ) :qx 32. ,%) !)':y=x:3. ,%) ) dy:ppy = x ln jx + x + 3j ; x + 3 (x > 0):arcsin x224.
C % % :0py = x ; 20 x = ;8:320291! 71. ,%) !)':y = 12 ln(e + 1) ; 2 arctg e :2. ,%) !)':2xxy = (ctg 3x) x :3. ,%) ) dy:2ey = arctg(sh x) + (sh x) ln ch x:4. C % % :px1+y = 1 ; px x = 4:00! 81. ,%) !)':e + 11 :y = ln(e + 1) + 18e 6(+e 27+ 1)2. ,%) !)':2xxxx3y = x x:3. ,%) ) dy:; 1:y = arccos xx p2tge224. C % % :0py = 8 x ; 70 x = 16:40292! 91. ,%) !)':ppy = ln22 ( 2 ; 1 ; arctg 2 ; 1):2. ,%) !)':xxy = (tg x) x :3.
,%) ) dy:py = ln(cos x + 1 + cos x):4e244. C % % :0y = 2x ; 3x + 1 x = 1:20! 101. ,%) !)':pe ; 1:y = 2(x ; 2) 1 + e ; 2 ln p11 ++e +1pxxx2. ,%) !)':y = (cos 5x) x :3. ,%) ) dy:ppy = ln(x + 1 + x ) ; 1 + x arctg x:e224. < % % :y = x ; 3x + 6 x = 3:02x02293 " "! 11. ,%) & & ) :y = x + 16 ; 165 "15 4]:2x2. :) ! ) !% :y = x + 4:3x2! 21. ,%) & & ) :y = 4 ; x ; 4 5 "15 4]:x22. :) ! ) !% :y = x x;;x 1+ 1 :2! 31. ,%) & & ) :q3y = 2(x ; 2) (8 ; x) ; 15 "05 6]:22. :) ! ) !% :y = x +2 2x :2294! 41.
,%) & & ) :y = x2(;x 2+x +3)5 5 ";35 3]:2. :) ! ) !% :y = 3 4+xx :2222! 51. ,%) & & ) :py = 2 x ; x5 "05 4]:2. :) ! ) !% :x :y = 9 12+x2! 61. ,%) & & ) :q3y = 1 + 2(x ; 1) (x ; 7)5 ";15 5]:22. :) ! ) !% :y = x ;x ;3x1+ 3 :2295! 71. ,%) & & ) :py = x ; 4 x + 55 "15 9]:2. :) ! ) !% :y = 4 ;x x :32! 81.
,%) & & ) :x 5 "05 3]:y = 1 10+x2. :) ! ) !% :y = x ;x ;4x4+ 1 :22! 91. ,%) & & ) :q3y = 2(x + 1) (5 ; x) ; 25 ";35 3]:22. :) ! ) !% :y = 2x x+ 1 :32296! 101. ,%) & & ) :y = 2x + 108 ; 595 "25 4]:2x2. :) ! ) !% :y = (x ; 1) :2x229701 2 1. :) . ) !). / , '*% !).
< , '*% !), % .2. <% %. :) , !) . :) !) , !) !% .3. ,! . <% ! %. F! !% .4. G . ( %. H & ! !).5. < %. I &, . $ ! .6. /) !). 6 .7. :) . , ! .8. :) , % % . J% .9. K . K. ,) ) ). % ). ( !).10. ,! )% . :) ,!) . :) % . L !) .11. :) % . :) %.12. :) ) & ! ).13. M, ! . <% %, ! .14. / ) (> , L, 6&), % .15. : L! ) !).16. J .29817.
G . ,) . K ! !% !)%.18. M (% L :.19. :) % e , sin x, cos x, ln(1 + x), (1 + x) ! (%. / . : (% ) ! %.20. ,! !. ( !. ,) . K . 9) ! &% !)%.21. 9) !*' !) &! ). K ! % !)%.x299 311. M, ! . <% %, ! . ( > .2. G . ( %. H & ! !). 321. ,! !. ( !. K .2. :) % . :) %. 331. M (% L :.2.
:) , % % . J% . 341. /) !). 6 .2. G . ,) . K ! !% !)%.3001. ! .., 6!7 .. / .C.: ,, 1982.2. 89:9 .;. C% . C.: $&. &.,1981.3. < ) ! ) . N.I. L% : J ! ) // :) ). F.$. K)a I.:. C.: ,, 1993.4. ! .. < ) ! .C.: ,, 1985.5. 86!:9 .. < )% ! &% (! ). C.: $& &, 1994.301 ;<:) ...................................................................................... 3L6P99 1.
$) % ........................... 79'" !# .!"#! .................................... 7:! % .!"#! ................................ 119'# #%! .'"# .!"#! ............... 14:! .!"#! .............................. 18;% .!"#! ........................................ 20 ....................................................... 22 2. :) ............................. 236!#% #"% !#%2 1!# ..................................... 239'"% # !! ...................................... 23<!.% $' .............................................
29 ....................................................... 31 3. :) ......................................... 336"!' .'"% ....................................... 339'" # .................................................... 35:! ............................................. 41 ....................................................... 45 4.
,! ............................................ 46= .''%#! ''%# ................... 46>% !#!# .''%#%2 .......................... 49 ....................................................... 53 5. <% %, ! ........... 559 .''%#! ' ......................
553#!# , .''%#%2 ' .......................... 56 ....................................................... 60 6. I ........................................ 61:! % 2 !#!# ............................ 613# 1" ! % ! .....................................................................3'# ! %2 .................................6364 ....................................................... 68 7.
G ............. 696!#% !#!# &##%2 ......................... 69302?!# &##! ...................................................74 ....................................................... 75 8. :) ................................................ 76-' !! " .' ...... 769 .'#" ........................................................ 76@'! '.' .'#" ........................ 77;2! !%! .'#" ....................................... 796"!' .'#"% .............................................. 802" !# !)!## .'#" .................. 80=' .'#"%2 !%, .'#" !$"#2 .................................................................. 819'#"% &'%2 .................................. 84 ......................................................
86 9. K ............................................. 88-''! ........................................... 882" "! !# "''! ...... 882" !# "''! .......................... 89@'! !%! "' ................................ 90-' !%, .'#" !$ .................... 919' "' # .'1%2 #%!2 ..... 929'#" !1 ........................................... 93#'! (!) '% .'#$"' ................................................................94 ....................................................... 95 10. :) % . ( * % ...........................
97=' .'#" ' ........................... 97@'! !%! .'#" ' ........... 99@.'! ................................................. 99@' $.'!2 .................................... 1009'#"% ..................................................................
101= .'#"%2 ....................................................... 101 ...................................................... 102 11. L ) .................. 1039'#"% "'% #%!2 .'"# ................. 103C' > .......................................................... 104-'% #%!$ .'" ...................................... 105303' #'! '% .! " "'# .'" #% .'#$ ............................................ 106C, "% .''!, 2 "''# 106 ..................................................... 108 12. / ) ................................................................
109D!'% .'"! ........................................... 1149'# >. ("'$ #"% .'"!) ............ 117 ..................................................... 119 13. M (% .................................................... 121C' =' ! !% # ' 9 ........
124C' ;' " sin cos ln(1 + )(1 + ) ......................................................................... 125E!% ! .............................................................. 1279' '% =' .......................................... 128F%! .'"# ! .)( '% =' ............. 128xe xxxx .....................................................
129 14. G ............................................. 131!!"# . ?!# #'! %# ....................................................................... 1312" "! !# ! ] ......................................................................... 132-!% !# !'$ ! ...................... 133-! !# #'! (%#) # .........................................................................
133G!'% ..................................................... 1342" !# &!' ...................................... 134 ' ...... 135-!% !# &!' ...................................... 135!!"# &!' ! .)( #%!2 .'#"%2 137a b ..................................................... 137 15. : .............................
139.'# #%.! $' . = .'$ .. 139-!% !# #%.! (#$!) .................. 140-!% !# .'$ ................................ 1412" !# .'$ ................................. 1426) . !!"# .!' $'# ... 143 ..................................................... 146304:>F6(9N<69 HF,Q(9Q 1. :) !) .................................... 1499 .'" !# .!"#! ............... 149:! % .!"#! ............................. 151:! .!"#! .......................... 1529'% 21" .'"# "', !"'1)2''! ........................................................156 2.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
