数学分析数学分析数学分析 (16).pdf

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1、?10.4?1.?Taylor?1+2x?3x2+5x3?x0=1;?21x?x0=?1;?22xxx?x0=?;?sin x?x0=6?;?ln x?x0=2;?34x?2?x0=?;?11?xx?x0=?;?(1+x)ln(1?x),x0=?;?lnxx?11?x0=?;?xx?1e,x0=?1?tx?1?1+2x?3x2+5x332)1(5)1(3)1(21?ttt32512115ttt?32)1(5)1(12)1(115?xxx?),(?D?2?)1(111?xx?0)1(nnx?21x?11)1(nnxn?0)1)(1(nnxn?1?R?2?x0?x)0,2(?D?3?22xxx?)

2、1)(2(xxx?()$%&?xx221131!#+,-?002)1(31nnnnnnxxnnnnx?!#+,-?012)1(131?1?R?1=?x)1,1(?D?4?sinsin()66xx?)6cos(6sin?xcossin()66x?1201(1)()2(2)!6nnnxn?2103(1)()2(21)!6nnnxn?R?),(?D?5?lnln2(2)xx?()$%&?221ln2lnxnnnnxn)2(2)1(2ln11?2?2?R?4?x?11)1(2lnnnn?0?x?112lnnn?4,0?D?6?324x?2?343221()$%&?xnnnnxn2023312)1(4(

3、)$%&?2?R?2=?x()$%&?nnn31)1(403?()$%&?nunn31)1(?()$%&?1lim1nnnuun?()$%&?113)1(3limnnnn134?Raabe?2,2?D?7?11?xx?2?211121xx?nnnnxx)1(2)1(210nnnnx)1(2)1(11?2?R?3?x1?x)3,1(?D?8?11(1)ln(1)(1)()nnxxxxn?nnxnnx?()$%&?2111?1?R?2?1?x1?x?*?1,1?D?9?1ln1xx?*1ln(1)ln(1)2xx?111(1)12nnnnxxnn?-#?120121?nnxn?+!,?1?R?1=

4、?x)1,1(?D?10?xx?1e?2?00!)(nnnnxnxnnnxn?()$%&?2!)1(!41!31!211?nxna!21!31!21?na?)4(.n?1?R?1=?x)1,1(?D2.?x0=0?Taylor?xxsin?4x?xsine?4x?ln cos x?x6?xx?11?x4?(1)?xxsin?53120161xxxx2411116120 xx&)?$%(?241116120 xx&)?$%(?224116120 xx&)?$%(?241716360 xx?(2)xsine?xxxx432sin241sin61sin21sin1 3()$%&?3611xx2361

5、21()$%&?xx336161()$%&?xx?()$%&?4361241xx?4281211xxx?(3)lncosln1(1 cos)xx?32)cos1(31)cos1(21)cos1(xxx()$%&?4224121xx2422412121()$%&?xx?()$%&?3422412131xx?642240712121xxx?(4)xx?11)(21432?xxxx)(1432?xxxx232)(21?xxx32)(21?xx4)(2415?x?4328321211xxxx?3.?0.001?F10dsinxxx?F102dcosxx?F210darctanxxx?F?231dxx?

6、(1)F10dsinxxxF?1002d)!12()1(xxnnnnF?1020)!12()1(dxxnnnn?0)12()!12()1(nnnn?Leibniz?)12()!12(1?nnun?3u00003.04F10dsinxxx?30)12()!12()1(nnnn?(2)F102dcosxxF?1004d)!2()1(xxnnnnF?1040d)!2()1(xxnnnn?0)14()!2()1(nnnn?Leibniz?)14()!2(1?nnun?3u0001.04 4?F102dcosxx?30)14()!2()1(nnnn?(3)F210darctanxxxF?21020d12

7、)1(xxnnnnF?21020d12)1(xxnnnn120221)12()1(?2?nnnn?Leibniz?12221)12(1?2?nnnu?3u00016.04F210darctanxxx?1230221)12()1(?2?nnnn?(4)F?231dxxF?()$%&?23311dxxxF?2131)1(dxxnnnF?2311)1(dxxnnn?11312)13()1(nnnn?Leibniz?132)13(1?nnnu?4?4u00004.0F?231dxx?411312)13()1(nnnn?4.?xx1e?x=0?1)!1(nnn=1?xex1?)1!(10nnnxx?11

8、!nnnx?0)!1(nnnx,?21xexexx?11)!1(nnnnx?1?x?1)!1(nnn=1?5?1?()$%&?12122)1()1(nnnxxnn?5?2?()$%&?11211nnxn?(1)?111)1()1()(?2?nnntnntf?tttfnnn?11)1()(111?)1ln()(ttf?F?tdtttf0)1ln()(ttt?)1ln()1(?1)1ln()11()1()1(11?2?tttnnnnn?1,1?t?222()$%&?xxt?1)2()4(2ln)2()4(222)1()1(2222211?()$%&?xxxxxxnnnnn,?0,?x?(2)?Ca

9、uchy?()$%&?nnxn11211?()$%&?0nnx()$%&?1nnnxxx?11ln11,?)1,1(?x6?na1?b?1nnnba?dncan)1(?,?,2,1?n?1nnnba?11nnbc?21nnbnd?11111111?2?bbbbnn?221)(?nnnxbnxf?F?xnnnbxdxxf021)(bxbx?2?112)(xbbx?2)(1)(xbxf?622)1(1)1(1?bfbnnn?1nnnba?11nnbc22)1()1(1?bdbcbndnn?7?F?1021lndxxx?FF?F?01021002102ln)ln(1lnnnnnxdxxdxxxdxx

10、x?02)12(1nn?10.4.6?61212?nn?41?24)2(1212?nn?8)12(1202?nn?81ln2102?Fdxxx?8?(1)?4?=arctan21+arctan31,?410?(2)?6?=arcsin21,?410?(1)?(4arctan21+arctan31)?!#+,-()$%&?1121213121124)1(nnnnn?Leibniz?()$%&?12123121124nnnnu?7u000038.07?!#+,-()$%&?71121213121124)1(nnnnn?1416.3(2)6?arcsin21?2?11221)12(!)!2(!)!12(21nnnnn?1221)12(!)!2(!)!12(?2?nnnnnu?6nnu?61221131nn?0000125.07 76?arcsin21?2?611221)12(!)!2(!)!12(21nnnnn?1416.39?F?311dxex?410?F?311dxexF?310!)1(dxxnnnnF?310!)1(dxxnnnn?()$%&?21311)1(!)1(3ln2nnnnn?Leibniz?()$%&?1311)1(!1nnnnu?000033.07?u?8F?311dxex?()$%&?721311)1(!)1(3ln2nnnnn?8