Контрольные работы по математическому анализу

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. . . 2005 2 517 - : . / . . . , . . . . : , 2005. 34 c. -, . , - , , . : - . . , - . . : - . . . . . , 2005 31. 4 2. 10 3. 14 4. 16 5. 22 6. 26 7. 30 8. 33 4. b )(xfy = , Xx , a , ,...,2,1, = nXxn , axnn=lim - )}({ nxf )(xfy = ,...,2,1, =nxn b bxf nn=)(lim , bxfax=)(lim . , a b + : +=)(lim xfax, bxfx=)(lim , =+)(lim xfx .. 1sinlim0= xxx, . . : 1. 3233542limxxxxx +++ 2. 623lim2232 ++ xxxxxx 3. 324238lim3535+++ xxxxx 4. 125103lim325 xxxx 5. 6264265453limxxxxxxx ++ 6. 23123limxxxxx + 7. 3232354543limxxxxxxx ++ 8. 1212lim221 + xxxxx 5 9. 45756742435limxxxxxxx +++10. 2732lim323 ++ xxxx11. 52243lim532+++ xxxxxx12. 112lim321 +++ xxxx13. 563739lim234++ xxxxx14. xxxxx 224lim222 +15. 3232425723limxxxxx ++16. 55245lim25 xxxx 17. 635522132lim2434+++ xxxxxx 18. xxxxx 224lim222 +++19. 3 23 56 36 2532limxxxxx +20. 329lim223 xxxx21. 458568244limxxxxxxx +++22. 12lim321 + xxxx23. xxxxxx 255lim3 53 23++24. 641252lim324 xxxx25. 345823lim2525+++ xxxxx26. 1lim331 xxxx27. xxxxx ++ 3 54 24 5 423lim 28. xxxx 28lim232 ++29. 34554lim3 53 23 5+++ xxxxxx30. xxxxxx 85273lim5 33 433 2+++ 6B. : 1. + 1212lim223xxxxx 2. 9631lim23 xxx 3. 31 1311limxxx 4. 4221lim22 xxx 5. 1211lim21 xxx 6. ++ 4421lim22 xxx 7. ++xxxx3lim 2 8. ++ 1513lim31 xxx 9. ++ 27432lim33 xxx 10. +22lim axxx11. + 11lim223xxxxx 12. 25154lim25 xxx 13. ++1lim 2 xxxx 14. + 16342lim24 xxx 15. 64587lim 28 xxx16. ++xxxx2lim 2 17. 81221lim 32 xxx18. +xxxx41lim 22 19. xtgxxx222cossinlim 20. 16641lim24 xxx 21. ++xxx3lim 2 22. 13lim234xxxxx 23. +++xxxxx22 1lim 24. 16641lim24 xxx 725. +++53lim 2 xxxx 26. 36368lim26 xxx 27. +xxxx 1lim23 28. 2sin41sin1lim220 xxx29. +++xxxxx342lim 22 30. +++ 2224)23)(12(123limxxxxxxx C. , : 1. xxtgx5lim0 2. xxx 4sin3sinlim0 3. xxtgx 27lim0 4. xxx 3sin8sinlim0 5. xxx 37sinlim0 6. xxx2sinlim0 7. xtgxx 25lim0 8. xxx 4sin9lim0 9. xtgxtgx 65lim0 10. xxctgx5lim011. 23lim0xctgxx12. xctgxtgx43lim013. xctgxctgx 72lim0 14. xctgxxtgx 32lim 20 15. 220 45sinlimxxx 16. xtgxtgx 65lim0 17. 220 53cos1limxxx 818. xxx 4cos17lim 230 19. xtgxx 75sinlim0 20. 32lim220 xtgxx21. xxtgx 43lim0 22. xctgxctgx 36lim0 23. xxx 52cos1lim2024. xxx 3sin7lim20 25. xctgxtgx75lim026. xctgxtgxx 43lim 20 27. xtgxx 53sinlim20 28. 204sinlimxxx 29. 206lim xxctgx30. xxx 3cos12lim 220 D. , : 1. xxxx 230 sin34lim 2. xtgxx 65sinlim0 3. )1ln(3lim0 xxtgx + 4. xexx 4sin1lim0 5. 1lim 20 xx ex 6. )1ln(3sinlim0 + xxx 7. )1ln(3lim0 xxtgx + 8. xxx3sinlim0 9. xxx ln1lim110. 20cos1limxxx 911. xxxtgxx sinsinlim0 12. xxxlnlim13. xtgtgxx 3lim214. ctgxxxlnlim015. 30sinlimxxxx16. bxaxx cos1cos1lim0 17. xee bxaxx sinlim018. 30limxarctgxxx19. xtgxx 2cos1lim420. 311lnlimxxx 21. xxx 42sinlim0 22. xctgxx 43lnlim0 23. xe xx 3sin1lim2024. )3ln(5sinlim0 + xxx25. 12lim 320 xx ex26. 230 232limxxxarctgxx +27. xexx 5sin1lim028. 20 43cos1limxxx29. xxxtgxx 3sin42sinlim0 30. 2204sinlimxxx 10.. )(xfy = x )()( xfxxfy += x , - : xyxxfxxfxx =+ 00lim)()(lim , )(xfy = - x ; - . + , , )(xfy = x -, , - . y , )(xf , dxdy, dxxdf )(. - . A. : 1. 263424+= xxxy 2. xxxy += 332 5 3. 32 3121xxxy += 4. xxy 21 += 5. 2321 3 += xxy 6. ( )2xxy += 7. ( )2xay += 8. 2311 =xy 9. 4 33 253xxy = 10. xtgxy cos32 = 11. xexy 5sin7 += 1112. ctgxxy += 13. 5 32ln xxy += 14. 3 xxey x = 15. 4cos1 xy = 16. tgxxy 6sin2 = 17. 3ln5xeyx= 18. ctgxxy += 4 19. xxey x ln3121+= 20. 32sinxxy = 21. 43 2 xxy = 22. 4ln xtgxy += 23. 5sin2 ctgxxy = 24. 53 235 xxxy ++= 25. xxey x sincos += 26. 22 12 +=xxy 27. 213 +=xxy 28. 44 5332 xxxy ++= 29. 243 211=xxy 30. 3ln1 xxey x ++= B. : 1. xxy cossin = 2. xxxy ln)( 2 += 3. xetgxy = 4. xctgxy cos= 5. += xxxy2sin 6. ( )2cossin xxy = 7. 11+=xxy 8. xxxysin22 = 9. 2cos+=xxy 1210. xtgxy = 11. xxeyxcos3 4= 12. 11322+=xxxy 13. ( )2sin xexy += 14. ( )xxyln1 2= 15. xxxeyxcossin2= 16. tgxxxy 3ln = 17. xxtgxy cos+= 18. xxy sin3 4= 19. xexy 2)1( += 20. 14322 +=xxy 21. ctgxxxy 4sin = 22. += 23cos xxxy 23. tgxxy = sin 24. xctgxy cos= 25. xexy 2)23( += 26. xxxtgxy2cos3 += 27. ( )2cos xexy += 28. ctgxxtgxeyx=229. 2sinxexyx= 30. )( 2 xxctgxy= C. : 1. 43sin3 xy = 2. xy 5cos2= 3. xxy 5cos3sin = 4. ( )22cos3 xxtgy += 5. )2( 23 xxctgy = 6. 3 3sin xy = 7. )23( 2 += xxy 13 8. xxy4cos5sin= 9. 132+=xeeyxx 10. )23ln( 4 += xxy 11. 5)14(sin += xy 12. 3 2)3sin2(1xxy= 13. 1cos1sin+=xxy 14. )21ln(12xxy+= 15. 7)4cos1(1xy+= 16. )3ln(522xxtgy += 17. )(2sin12xxxy= 18. 411bxaxy+= 19. 125ln+=xxy 20. 1cos)12sin(+=xxy 21. 3)34( += xtgy 22. xxy2cos)13sin( += 23. 3)2cos1(1xy+= 24. )3sin(12lnxxy += 25. 3 4)32(ln1xtgxy= 26. xxexy 324)3sin( = 27. )ln(2124xxxy= 28. xxtgy5cos31 2+= 29. 3 3 32sin= xexy 30. ))23ln(cos( 2 xxy = 14 - . )(xfy = ( ) 0x , )( 0xf - . .. )(xfy = 0x , )(xfy = 0=y . .. )(xfy = 0x 0x , , 0x , 0x : y + -, 0x - ; y - +, 0x - ; y , . A. : 1. 21 xxy+= 2. 211xy= 3. 12 =xxy 4. 122=xxy 5. 322 )1(32 = xxy 6. 241 xxy += 7. 22 1xxy += 8. 233 xxy= 9. 3)1( xxy = 10. 32)1()1(+=xxy 1511. 2)1(12=xxy 12. 23)1(2 +=xxy 13. 43 )1( xxy = 14. 32 )1( = xy 15. )2)(1( 2 = xxxy 16. xxy = 3 2 17. 3223 )4( = xxy 18. 422 xxy = 19. xxy = 1 20. 23 2+=xxy 21. 31362+=xxx 22. 343xxy = 23. 3 2)4(1 = xy 24. )1(2 xxy = 25. 3455xxxy += 26. )4)(1( =xxxy 27. 23 )2( += xxy 28. )1()1(22+=xxy 29. )1(422 = xyx 30. )2)(1(22 = xxyx 16 - . )(xFy = )(xfy = , x )()( xfxF = .. . dxxf )( CxF +)( - )(xfy = ( C - ) : CxFdxxf += )()( . , - : = vduuvudv , )(xuu = )(xvv = - , - )(xu )(xv . . A. : 1. + dxxxx 242 2 2. + dxx 2)2( 3. dxxx 13 2 4. + dxxx3cossin 5. xdx2cos 6. + dxxx 23 17 7. + dxxx )( 3 8. dxxx322 )1( 9. + dxxx 4 31110. dxxeexx21 11. +dxxeexx2cos1 12. dxxxctg22cos2313. + dxxx 3253 2 14. dxxxtg22sin415. dxxx23coscos216. dxxx32)1( 17. dxxxx424 3 )( 18. dxxx2312 19. ++ dxxxx 3232120. + dxxxxx3 24 54 34 2 21. xdx2sin3 22. dxxx422 )9( 23. dxxx323 2 )1( 24. dxxxx34 34 23 25. dxxx2432526. + dxxx23 2 1 27. + dxxxx 32 3128. + dxxxx423 5329. dxxx23sinsin1 1830. + dxxxx23B. , : 1. + dxx 4)23( 2. dxe x3 3. dxx32sin 4. xdx4cos2 5. +13xdx 6. dxx53 7. + 34xdx 8. + dxx3 57 9. + )16(sin2 xdx10. dxeexx 23 11. dxxctg )3( 12. )92(cos2 xdx13. ( ) + dxx4 357 14. dxxeexx322 1 15. + dxx 53)15( 16. + dxxtgx )3cos( 17. ++ dxxx)14(sin)14(sin523 18. dxxxtg3sin332219. + dxx32312520. dxxtg )12( 21. )12(sin32 xdx22. + dxeexx332 1923. ( ) + dxx5 237 24. + 3)14( xdx 25. ( ) + dxx3453 26. dxxctg )25( 27. dxx )14sin( 28. xdx83 29. 6)23(4xdx30. + dxx7523C. : 1. xdxxsin 2. xdxx 2cos 3. dxxe x3 4. xdxx 2sin)4( 5. dxxe x 6. dxxx 2sin 7. dxxx )13cos( 8. xdxx 5sin2 9. dxex x22 10. xdxln 11. dxxx )1ln( 12. + xdxx sin)3( 13. xdxx cos)2( 14. dxex x2)5( 15. dxxx )52sin(2 16. + dxxx )14cos(2 17. + dxx )1ln( 2 18. + dxxx )1ln(2 2019. dxxx 2sin2 20. dxex x2)13( 21. xdxx 5sin)42( 22. dxxex24 23. + dxxx )57cos( 24. xxdx4cos2 25. xxdx5sin 2 26. + dxex x3)42( 27. xdxx 4cos)3( 28. + dxex x2)4( 29. + dxex x2)1( 30. xdxx 3sin7 2 D. - : 1. + dxxx922 2. + dxxxxx41432 3. ++ dxxxx)12)(1( 4. ++ dxxxxxx)4)(3)(1(91412 2 5. dxxx1632 6. + dxxxxx25432 7. + dxxx9)2(2 8. dxxxx232 2 9. dxxxx324110. + dxxxx23 24 11. + dxxxx6552242 12. +++ dxxxxxx)12(2322 13. dxxxx)64(322 14. +xdxxx 212 2115. + dxxxx233 1 16. + dxxxx)2)(3(12 17. + dxxxxx48345 18. ++ dxxxxx222)1)(9(6219. +++ dxxxxxxx2223)2()3(142520. dxxxx)1()1( 22521. dxxxx)9)(2(4 22. ++ dxxxx2722 23. + dxxxxx32 323 24. + dxxxx23)1( 25. dxaxx3323 26. +++ dxxxx102252 27. ++ dxxxxxx232215228. + dxxxxx5215723 29. +++ dxxxx44124 30. ++ ))(( bxaxdx 22 - . )(xf = - ],[ ba , - - : )()()( aFbFdxxfba= , )(xF )(xf = ],[ ba . A. : 1. +102 )123( dxxx 2. 412xdx 3. 143xdx 4. 22)1(cos dxx 5. 91)(3 dxxx 6. +2121 dxxx 7. +94)1( dxxx 8. 213 )( dxxx 9. +30)1( dxex 10. 813 2xdx 11. +2142 1 dxxx 12. adxaxx02 )( 2313. +813 23 2 1 dxxx 14. +402)1( dxx 15. +0)3(sin dxx 16. 682 2cos xdx17. +103 4)83( xdx 18. +101 dxx 19. aaaxdx22 20. 1325 4)3( xdx 21. 303sin xdx 22. dxex303 23. 1024 xdx 24. 2122 dxx 25. 404sin xdx 26. +1014xdx 27. 692 3sin xdx28. +103)31( xdx 29. +831 dxx 30. dxee xx4024 2 24B. - : 1. 10dxxe x 2. +322 232 xxdx 3. 342sin xxdx 4. +212 127xxdx 5. +10)1ln(edxx 6. 212 54xxdx 7. 342cos xxdx 8. 312 43xxdx 9. 0sin xdxx 10. +30)3ln(edxx 11. ++102 56xxdx12. 802 2sin xxdx13. +412 23 xxdx14. 202dxxex15. 1312 16 xxdx16. 20cos xdxx 17. 212 32xxdx 2518. 02 sin xdxx 19. ++102 3103 xxdx20. 4222 dxex x 21. ++322 78xxdx22. 202sin xdxx 23. +4232952 dxxxxx24. +50)5ln(edxx 25. ++522 363 xxdx26. +40)4ln(edxx 27. ++312 13412 dxxxx 28. +424cos)1( dxxx 29. +++21)3)(2)(1( xxxdx 30. ++322 12xxdx 26 , )(xyy = , 1xx = 2xx = , =21)(xxdxxyS , )(yxx = , 1yy = 2yy = , =21)(yydyyxS , , - )(xyy = , 1xx = 2xx = , =212 )(xxdxxyV , , - )(yxx = , 1yy = 2yy = , =212 )(yydyyxV A. , : 1. 0,42 =+= yxy 2. 0,32 =+= xyx 3. 0,4,1,4 ==== yxxxy 4. 0,2,1,22 ===+= yxxxy 5. 0,,0,sin ==== yxxxy 6. 0,5 2 ==+ xyx 27 7. 01,122 =+= yxxy 8. xyxy == 8,7 9. xyxy == 2,2 10. 2,4 2 +== xyxy 11. 2,42 == xyyx 12. xyxy == 5,4 13. 22 2, xyxy = 14. 0,422 =+= xxy 15. 0,8,32 === xyxy 16. 0,6,1,6 ==== yxxyxy 17. 2,4 2 == xyyx 18. 0,6 2 == yxxy 19. 0,4,4,22 =+==+= yxyxyxy 20. 0,5,2,5 ==== yxxxy 21. 4,4,22 +==+= xyxyxy 22. 0,3,0,1 ===+= yxxxy 23. 5,12 =+= yxy 24. 0,4,2 === yxyx 25. 0,2,3 === yxxy 26. 0,6,42 === yxxy 27. 4,32 == xxy 2828. xyxy == 7,6 29. xyyx == 2,4 2 29. 0,2,2,cos ==== yxxxy 30. 4,42 +=+= xyxxy B. , , - : 1. 3,0,42 ==+= yyxy 2. 4,0,52 ==+= xxyx 3. 0,3,1,3 ==== yxxxy 4. 0,4,2 === xxxy 5. 7,1,12 ==+= yyxy 6. 0,4,1,4 ==== yxxxy 7. 0,)4( 32 =+= xxy 8. 0,42 == xxy 9. 2,0,)1( 2 === yxxy 10. 1,cos == yxy 1=y x 11. 0,4, === yxxxy 12. 0,sin == yxy x0 13. 0,7,2 === yxxy 14. 8,0,3 === yxxy 15. 2,122 == xyx 2916. 4,2 == yxy 2=x 17. 3,03)3( 2 ==+ xxy 18. 0,1,2 === yxyx 19. 0,2,1,2 ==== yxxxy 20. 0,2,3 === yxxy 21. 0,2,2 === yxxy 22. 0,3,0, ==== yxxey x 23. 2,422 == yyx 24. 0,2,0,sin ==== yxxxy 25. 2,2,3 === yyxy 26. 0,4 2 == xyx 27. 2,52 == yxy 28. 3,0, === yxxy 29. 0,7,1, ==== yxxey x 30. 3,2,3 === xxyx 30. )(xfy = , - ),[ +a - ],[ ba badxxf )( +b : ++=babadxxfdxxf )(lim)( . +babdxxf )(lim , +adxxf )( , - , . bdxxf )( , =baabdxxfdxxf )(lim)( . - : +++=dxxfdxxfdxxf )()()( , . 31A. : 1. +12xdx 2. +1xdx 3. +1xdx 4. +15xdx 5. +0dxe x 6. +0cos xdx 7. 0dxex 8. ++42 32xxdx 9. +1322 dxex x 10. +153 4)32( xdx 11. +13 xdx12. +02sin xdx 13. +2lnexxdx14. +02 dxe x 15. ++12 xxdx16. +1dxxe x 17. +022 dxexx18. +exxdx2ln19. +02dxxe x 3220. ++144 5)2(xdx 21. +05 dxe x 22. ++52 86xxdx23. ++214xdx24. +1ln xxdx25. +23cos xdx 26. ++42 44xxdx27. +103)53( xdx 28. +114 dxe x 29. +++02 144 xxdx30. ++06)23( dxx 331. . . . .: , 1985. 383 . 2. . ., . . -. .: , 2001. - 304 . 3. . ., . ., . . - . 1. .: , 1999. - 304 . 4. . ., . ., . . - . 2. .: , 1999. - 416 . 5. . ., . . . 1. .: , 1998. 616 . 6. . ., . . . 2. .: , 1998. 448 . 7. . . . . 1. .: , 2002. - 400 . 8. . . . . 2. .: , 2002. - 424 . 9. . . . .: , 1971. - 352 . 10. . . . . 1. .: -, 2004. 416 . 11. . . . . 2. .: -, 2004. 544 . 12. . . . .: - - -, 1973. 472 . 13. . . . . 1. .: , 2002. 448 . 14. . . . . 2. .: , 2002. 464 . 3415. . . . .: , 1999. 176 . 16. . . . .: , 2004. 304 . 35 : - . . , - . . ___________________________________________ . 60 84 1/16. . . . . . 300 . . . . . . . 603600, -20, . , . , 23. , 603000, . , . . , 37.

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