1、2000 M S V 3 dB I k = k5W# Ba A b5 1()30arctanlimln 1 2xx xx=+. s 16 . W ()232300011arctan arctan1lim lim lim26ln 1 2xxxxx xxxx+=+()2220lim6116xxx x=+=2 !f ()yyx= Z 2xyx y=+ 50|xdy= . s ()ln 2 1 dx W ZEB s TMX T H H ps ()2ln2xyydx xdy dx dy+ =+ Z 0x = H 1y = | T ln 2 ,dx dx dy= ( )0ln 2 1 ,|xdy dx=
2、ZE= Z 2xyx y=+ H x p 2ln2 1xydy dyyxdx dx+ =+| 0x= Z 1y = | 0x= 1y = T ()ln 2 1 0 1dydx+=+ 考研数学助手您考研的忠实伴侣 ln 2 1dydx= ( )0ln 2 1 ,|xdy dx= 3()272dxxx+=+. s 3W 7 2,x t=522, 2 ,x tdxtd=+ = () ()22200022lim99722lim arctan333|bbbbdx tdt dttttxxt+ +=+=4 wL()121xyxe=|vLZ . s 21yx=+ W y ()111111lim lim 2 2
3、lim 2 lim 2 121lim 11xxxxxxxxxxyaebyx xeeeex = = =#vLZ 21yx=+ 5 !100023 00,045000 67AE= 4 O ()()1B EA EA= +,5 ()1B E+“ . s 100012 00023000 34W ()()1B EA EA=+ ()E AB E A+= ()()2,2,AB A B E EEAEB E+=+=9 ()()1,2EAEB E+= # ()()1100012 0010230200 34BE EA+=+=a45 1 !f ()bxxfxae=+ (), + = O ( )lim 0xfx= 5 ,
4、ab A 0, 0ab C 0, 0ab D 0, 0ab wL j . # ()()0, 0f wL ()yfx= . 3 !f () (),f xgx v , Vf O ( ) ( ) ( )()0,fxgx fxgx B ( ) ( )()()f xga fagx C()() ()()f xgx fbgb C ( ) ( )()()f xgx faga s A . W 5 ! ()()()() () ()()20fx f xgx fxgxgx g x = ()() ( ) ( )f xgb fbgx VnA . 4 ()30sin 6lim 0,xxxfxx+= 5( )206limxf
5、 xx+ A 0 B 6 C 36 D s C W ZEB y ()()331sin 6 6 63!x xxox= + () ( )( )()33330020636sin 6lim lim6lim 360xxxx xox xfxxxfxfxx+ +=+=Vn()206limxf xx+“ 36 ZE= y () ( )()3300320sin 6 sin 6 6 6lim lim6sin 6 6lim0xxxx xf x x x x xy xxxf xxx+=+ =+ = ()23 200 006sin 6 6 6cos 6 6lim lim lim312sin 6lim 362xx xxfx
6、xx xxxxx + = = =5 +12 3,2,3xxxyey xey e= = 3“ QsZ A 0yyyy+= B 0yyyy+ = C 61160yy yy+= D 220yyyy + = s B W +Z 12 31, 1 = = +Z ()()23211 10+=+= # pLsZ 0yyyy+ = Vn B a ! ()( )ln 1ln ,xfxx+= 9 ( ) .f xdxW ! ln ,x t= 5tx e= ()( )ln 1,ttefte+= V7 ()()()() ()() ()()()ln 1ln 11ln 1 ln 1 111ln 1 ln 11ln1xxxx
7、xxx xxxxxx xxxef x dx dx e deeeee dxee dxeexeCxe eC+=+= + = += + + + +=+ + + a ! xOy Z () ,|0 1,0 1Dxy x y=#L ():0lx y tt+ = ()StV UZ DL lP/Zs k p () ( )00.xStdtxW 5 ! ()221,0 12121,1 221, 2ttSt t t tt= + Vn 01x H ()230011;26xxStdt tdt x= 12x H () () ()20021xxStdt Stdt Stdt x=+=yN ()33201,0 1,611,1
8、2631, 2xxxStdt x x x xxx= + + a pf () ( )2ln 1f xx x=+ 0x = ) n ( )( )( )03nfn WZEB X T () () ()( )( )( )200002! !nnfffx f f x x xn= + + +“# () ()()23 21224213ln 1 123 21nnnnxx xxxxxnxxxn+= + +=+ +“1 nx “ ()() ()( )101!2nnfnn= ()()()( )11!02nnnfn=ZE= DG T ()( )()() ( ) ( ) ()()01 2 012 nnnn nnnuv u
9、v C u v C u v u v=+ + +“ # ()() ()( )()111!ln 11kkkkxx+=+k ()()()( )()()( )()()()( )()12 321211! 1 2! 1 3!21nn nnfxx nx nnxx x =+ + + V ()()() ()( )()131!01 13!2nnnnfnnn= =Ba !f ()0cos ,xSx tdt=1 n O ( )1nxn () ()000, cos 0,fxdx fx xdx= =# cos x 0, ()( )()()()()11101100coscoscos cos cos cos 0fx x dx
10、fx x dx fx x dx=+V7w( )0, =“1 ( ) 0fx= 6B L 2 #i 12, P ( ) ( )120.ff= = a X ()f x 5 f 0x = # = 1“ T ()() ( )1sin 3 1sin 8f xf xxax+=+ ()ax 0x H1 x kl O ( )f x 1x = ) V p wL ()yfx= ()()6, 6f ) MLZ . W ()() ( )1sin 3 1sin 8f xf xxax+=+ H |K ()() ( )00lim 1 sin 3 1 sin lim 8xxf xf x xax+ = + () ( )131
11、0,ff= ()10,f = y ( ) ( ) ( )001sin 3 1sin8lim lim 8sin sin sinxxfxfx axxxxx+ = + =Vn ( ) ( )()()()()() ()()001sin 3 1sinlimsin1sin 1 1sin 1lim 3sin sin13 1418xxfxfxxf xf f xfxxfff+ =+=+=# ()12f = ()()5,f xfx+= () ()610ff= ()1f i ()6f 9i O ( ) ( )612ff= = # p MLZ ()26yx= 2120xy = Ea ! wL ( )20, 0yaxa
12、 x=21yx= ,A VUS O AL wL2yax= B m a Hm xB 88Kv$ W 0x H221yaxyx = 1,11axyaa=+#L OAZ 1axya=+ 88 ()()1 222410122 23515021231 5 151|aaaxVaxdaaa axxaa+=+=+V7 () ()()()()()532225272521 1221514015 1aaa adVdaaaaaa+=+=+7 0,dVda= i 0a B 4a = 5iN8 4a = H |Kv Kv8 5221632515 18755V= EBa f ()f x 0,+ V ( )01f = O T
13、 () () ()010.1xfx fx ftdtx+ =+1 p ()f x 2 0x H T( ) 1xefx . W 1 5 ! ()()()() ()011 0.xxfxxfx ftdt+ = T H x p ()()( ) ( ) 12.x fx x fx+=+ ()()21df xxdxfx x+=+Hs () ( )ln ln 1 lnf xx x C= + + + 5 ! T 7 0x = () ( )000ff+= ()01f = ()01f = ()f x Vr T 1,C = # ()1xefxx=+2ZEB 0x H ()0,fx ()f x h ( )01f = ()
14、 ( )01.fx f =!() () ,xx fx e=5 () () ()00, ,1xxxx fx e ex=+=+ 0x H ()0x ()x 9F y7() ()00,x= () ,xf xe 8 0x H T ( ) 1.xefx ZE= y () () () ()001xftdt fx f fx=| ()f x ()01.1xxef xdtt=+ 0x H 0001.1txxtxedt e dt et =+ () 1xefx. E=a !11012, , 0, ,2180TTABB = , T pZ 22 4 42.BAx Ax Bx =+ W 5 ! 11012121,0 21
15、0211102TA = 111, , 0 2 2,21B=B ( )2428TT T TAAAA = = Ze 16 8 16Ax Ax x =+ ()82AEx= 7()123,Tx xxx= Td QLZF 121212310,220,1212xxxxxxx+ = += QZFY 12,1k=k i d QZFB+ *10,0,2T= pZY*,x =+ 1020112xk =+ k i E a X_ F12301, 2, 1110ab = _ F1231392, 0, 631 7 = M O3 V123, LV U p ,ab . W ZEB y1 2 L131232 =+ _ F123
16、, L1 O 21 2 BvL1F . _ F123, 123, M#123, LM1 V7 T 1230, 1210,110ab= =N 3,ab= 3 V123, LV UV7 V1 2 LV U 1 2 3 LM1 yN 12313, 2010,310b= =e 2100b= 15, 5.ab= ZE= y3 V123, LV U#LZF 123139206 131 7 0x bxx=9 M 139139 13 921206 1 0612 12 012631 7 0 010 20 3210006bbbbbbb #d QLZHq 3210,10 6bb= 5b= y1 2 L131232 =+ _ F123, 275 !123, 123, V7 12305, 1210,110a= = N 15.a =
