专升本高数知识点汇总

12y312030041sin21)()(xfxf)()(xfxf0limclim1limlim100xxxxxxsinlimsinlim000sinlimsinlimexxxxxx10111)(limlime101)(lim5n,m.,,7812391210mnmnmnbaXQxPmnx,,,lim000xPnxQmmnmnmnAxfxx)(lim0Axfxx)(lim0AxfxfAxfxxxxxx)(lim)(lim)(lim0000)()(limlim0000xfxxfyxx)()(lim00xfxfxx)()(lim00xfxfxx)()(lim)(lim)()(00000xfxfxfxfxfxxxx)(lim0xfxx)(lim0xfxx)(lim0xfxx)(lim0xfxx)(lim)(lim)(lim)(lim0000xfxfxfxfxxxxxxxx12112a,b3(a,b)212a,b(a,b)*1a,b=C)(xfba,)(xfba,)(xfba,0)()(bfaf)(xfba,0)(f)(xfyba,)()(bfaf0)(f)(xfyba,abafbff)()()(b)(xfyba,0)(xf),(ba)(xfab0*2304x,x,5678)(),(xgxfba,),(ba),(),()(baxxgxfcxgxf)()(0)(xf)(xf)(xf0x)()(0xfxf)(0xf)(xf0x)(xf0x)()(0xfxf)(0xf)(xf0x3xy)(xf),(ba0)(xf)(xf),(ba0)(xf)(xf),(ba0)(xf0)(xf)(xf0x0)(0xf1;,2312912101,(2))(xf0x)(xf0x0xx0)(xf0)(0xfxx)(xf0x)(0xf0xx0)(xf0)(0xfxx)(xf0x)(0xf0x)(xf)(xf0x)(xf0x0)(0xf0)(0xf0)(0xf)(xf0x)(0xf0)(0xf)(xf0x)(0xf)(xf),(ba),(,0)(baxxf)(xf),(ba),(,0)(baxxf)(xf),(ba)(xfAxfx)(lim)(xfyAy0x)(limxfx)(xfy0xx21111232134baxxfaxxfxx)(lim,)(limbaxy00)(ln)(xfexf000)()(limlim)(00000xfxxfyxfxxhxfhxfxfh)()(lim)(0000000)()(lim)(0xxxfxfxfxx0x)(0xf0xx)(0xf123yyu4(5)65vuvuuvvuvu)(2vuvvuvuxfy)(ufy)(xudxdududydxdy0),(yxF)()(tytx)(xfy)()(ttdtdxdtdydxdydtdxdtdxdyddxdxdyddxyd)()(22)()(xvxuyaealn)(ln)()(ln)(xuxvxueeyxv)(xf67812x=0x=012+C12123dxydydx2xyxy)()(xfxF)(xF)(xf)(xf)(xF)(xfCxFdxxf)()(dxxfdxxfdxfdxxf)()()()(cxfdxxf)()(baxtbax,4121xS=2S=312=3456m,Mmin,max,Mtaxaxtaxaxtaxxatansecsin222222tttt2222sectan1,1cossinvduuvudvniiixbaxfdxxf10)(lim)()(xfba,)(xfba,)(xfba,0)(xfbadxxf)()(xf,,bxaxbadxxf)()(xfba,0)(xfbadxxf)(badxxkf)(badxxfk)(badxxgxf)()(badxxf)(badxxg)(cabcbadxxgdxxfdxxf)()()(abaabadxxfdxxfabdx)(0)(1badxxf)()()(xgxfbabadxxgdxxf)()()(xfba,)()()(abMdxxfabmbam741t25126)(xfba,ba,))(()(abfdxxfbabadxxfab)(1)(xfba,xaxfdttf)())((xadttfx)()()(xfx)(xfba,)(xF)(xf)()()()(aFbFxFdxxfbaba)(xfaa,0)(xfaa)(xfaa,aaadxxfxf0)(2)(17dcS=9081yabx2ab3cacadxxfdxxf)(lim)(bccbdxxfdxxf)(lim)(ccdxxfdxxfdxxf)()()()(xf)(xgdxxgxfSba)()(ba,)(yx)(yxdyyydc)()()(xf)(xfxdxxfVbax2)()(xf)(xgxdxxgxfVbax)(22ydcx(4)ydcx:12)(yx)(yxydyyVdcy2)()(yx)(yxydyyyVdcy)()(22321,,aaakajaia321321,,aaaxyzkji,,xyz3100451231231,0,0,0,1,0,0,0,1kji232221aaa2322211cosaaaa2322212cosaaaa2322213cosaaaa1coscoscos222xyz),,(,),,(1110000zyxMzyxM),,(01010110zzyyxxMM321,,aaa321,,bbb332211,,bababa321,,aaa,cos332211bababa232221232221332211,cosbbbaaabababa002cos,cosc,sincccc,,:A,B,CA,B,C1A=0,B=0,yC=0,zD=0,0,()1,c,c321321bbbaaakjic0332211bababa00sin,sin0DCzByAxCBAn,,n0DCzByx0022221111DzCyBxADzCyBxAl:czzbyyaxxl000:000zyx,,cba,,ctzzbtyyatxxl000:0DCzByAxCBA,,234123123czzbyyaxxl000:cba,,0332211bababa0332211bababa1111111czzbxxaxxl:2222222czzbyyaxxl:21ll0021212121ssccbbaa,1l2l021212121ssccbbaa,21ll,212121ssssss,cosczzbyyaxxl000:0DCzByAxl0nsCcBbAa,l00nscCbBaA,l222222CBAcbacCbBaAsin011111DzCyBxA022222DzCyBxA:210021212121nnCCBBAA,1(2)(3)4AA12021212121nnCCBBAA12212121nnnnnn,cos222ayx2222Rczbyax)()()(1222222czbyax00xzyfl),(:z022),(zyxfzyx,,yx,Dzzyx,),(yxfzyx,),(yxfz),(00yx),(00yx),(yx),(00yx),(yxfz),(yx),(00yx),(yxfzAyxfyxyx),(lim),(),(00),(),(lim00),(),(00yxfyxfyxyx),(yxfz),(00yx),(yxfz121xyxfyxxfyxfxzxx),(),(lim),(0yyxfyyxfyxfyzyy),(),(lim),(0dyyzdxxzdz),(yxfz),(),,(),,(yxvyxuvufzxvvzxuuzxzyvvzyuuzyz0),,(zyxF),(yxfzxzz),(yxfz),(00yx0),(,0),(0000yxfyxfyx0),(,0),(0000yxfyxfyx),(00yx),(yxfz),(yxfz),(00yx),(00yx),(),(),(),(2yxfyxfyxfyxPyyxxxy,0),(00yxP0),(00yxfxx),(00yxf23412312,31D212=+34,=+(5)6(7)D1D:,0),(00yxP0),(00yxfxx),(00yxf,0),(00yxP),(00yxf,0),(00yxP0),(yx)(xy)(xy),(yxfz),(),(),,(yxyxfyxF0xF0yF0F),(00yx),(00yxniiiidDfdxdyyxf10),(lim),(),(yxfDdxdyyxkf),(Ddxdyyxfk),(Ddxdyyxgyxf),(),(Ddxdyyxf),(Ddxdyyxg),(DdxdyD21DDDDdxdyyxf),(1),(Ddxdyyxf2),(Ddxdyyxf),(),(yxgyxfDdxdyyxf),(Ddxdyyxg),(,),(MyxfmMDdxdyyxfmDD),(),(yxfD),(Ddxdyyxf),(Df),()()(,21xyxbxa2D311L=2L=3L=21L,2L3L)()(21),(),(xxbaDdyyxfdxdxdyyxf)()(,21yxydyc)()(21),(),(xxdcDdyyxfdydxdyyxfrdrddxdyryrx,sin,cos)(0)sin,cos(),(rDrdrrrfddxdyyxfbxaxy),(Ldsyxf),(dxxxxfba2))((1))(,(dycyx),(Ldsyxf),(dyyyyfdc2))((1)),(()()(tytxtLdsyxf),(dtttttf22))(())(())(),(()(xyaxbyLdyyxQdxyxP),(),(dxxxxQxxPba)())(,())(,()(yxcydyLdyyxQdxyxP),(),(dyyyQyyyPdc)),(()())),(()()(tytxtt123456112x2nLdyyxQdxyxP),(),(dttttQtttP)())(),(()())(),(()(xfy0),(yxf)()(ygxfdxdydxxfdyyg)()(1xyfdxdyuxyuxy0)(yxPdxdy)()(xQyxPdxdyCdxexQeydxxPdxxP)()()()(xfyn),(yxfyuyp,q(1)1(2)2(3)3(4)411(1)12312120qyypy)(xfqyypy21,yy0qyypy2211ycyc21,yykkyy,2121,yykkyy,2121,yy21,yy0qyypy2211ycyc1y)(1xfqyypy2y)(2xfqyypy21yy)()(21xfxfqyypy*y)(xfqyypyxcxcy210qyypy*2211yycycy)(xfqyypy0qyypy02qprr21,rrxrxrececyrr212121rxexccyrrr)(2121)sincos(212,1xcxceyirax)(xfqyypy02qprr0qyypyy343xn=xnk4C,Dk5=)(xfqyypy*y*yyy)(xfqyypyxnexPqyypy)(,,qp)(xPn*yxnkexQx)()(xQn02qprr210k)sincos(xBxAeqyypyx)sincos(*xDxCexyxki02qprriik10*y*yyy*2211yycycy2211ycyc