1、1AP微积分公式大全AP微积分考试为闭卷考试，考试时也不给任何数学公式。因此，熟练掌握考试大纲要求的微积分公式十分必要。为了帮助考生更快的掌握AP微积分的相关公式，本文总结了AP微积分考试当中常用的重要公式，供大家参考学习。Chapter1.FunctionadLimit1.5种基本初等函数图像性质1 1 1 1 1 1; ; :log:sin/cos/tan/cot/sec/cssin/cos/tan/cot/sec/csx aPoweryxExponentialyaLogarithmicyxTrigonometricyxxxxxxInverstrigonometricy xxxxxx =
2、= =2.4种表达函数的解析式()(); ; (); ()(),()()xftyfxparametric polarrf vectorrt ftgtygt = = = 3.3个重要极限0sinlim 1;x xx= 101lim (1) lim (1) +=+=x xx xe ex 0010 1 110 1 1 ()()lim lim ()() 0()mmm mmn nx xn n n anmbPxaxax axa nmQx bxbx bxb n =+= = Chapter3.Integral31.不定积分定义式() () ()();defintionfxdxfxCmethodfxfxC=+
3、=+ 2.求不定积分的四种方法11 2 1221(1) : ,1 lnsincos,cossin, tanln|cos|cotln|sin| ,secln|sectan| ,cs ln|cscot|sin(1), tan,11nn u uxFormulasxdxCaduaCnxdxxCxdxxC xdxxCxdxxCxdxxxCxdxxxCdx dx dxxCx xCxx x+ = =+=+ =+ = += + = + = +=+= 3.反常积分的两种形式(1)()lim ()()lim ()() () ()(2)()lim ()()lim ba abb baab ba ccaa cbInte
4、gralonaInfiiteIntervalfxdx fxdxfxdx fxdxfxdxfxdxfxdxIntegrandwithInfiitediscontiuitesfxdx fxdxfxdx+ + + + + = ()() () ()b cab c ba a cfxdxfxdxfxdxfxdx= + 4.定积分定义和运算法则(1) (, , , )(2) :()lim lim ()(3) :b i ia n nRiemansumleftrightidtrapezoidaldefinitonfxdx AfxxpropertiesofIntegral = = 4()() () ()() ()
5、b b ba a ab ba afxgxdxfxdxgxdxkfxdxkfxdx= = 0() () ()()0 () ()()0() ()2()()b c ba a ca a ba b aa a aa afxdxfxdxfxdxfxdx fxdxfxdxfxdxfxod fxdxfxdxfxevn = += = = 5.微积分两条基础理论() ()()()() ()() () (),;b ba axafxdxfbfaorfbfafxdxdAxdftdtfxabdxdx= =+= = 6.定积分应用2 21 12 22 2()(1) :()()(2)( / / ),(3) (/ / / sec
6、),(4) : () ()()(bax yx yfxdxMeanvaluetheoremfcbaAreaverticalslicehorizontalslicepolarVolumediskwashershelknowncros tiondy dxLengthofcurveL dx dydx dyorLxtyt=+ =+ = + )( )dtparmetricequation7.微分方程(1) ();()(2) : (1) lim ;1: kx tdySepartionVarible MxdxNydy y KLogisticequationky yDifernti andyKdx K Aale
7、quation e = =+1 1 0 0 0(3)(4) : ()()()()( )nn nSlopefieldEluersmethodyyhyorfxfxfxxx =+ =+ 5Chapter4.Seris1.级数的定义与收敛性1231 123111:(1) ;(2): .;(3)lim , ;lim , .n nn nn n nnn nn nn nn naaaaapartialsumSaaaaaIf SexitstheaconvergesIf SdoesnotexitheadivergesDefinition= = =+=+2.判定级数收敛性的三大审敛法1111(1) :lim(1 ,
8、1 , 1 );(2): () , 1,): (nnnn nnnnaRatioaaconvergencedivergencemayconvergenceordivergenceIntegralIfafnispositvecontinuousanddecreaingforxtheaandfxdxbothconvergThrete nces et += = = 1 11 1;(3) : 0 , ;, .nnn nn nn nn nordivergerenceComparisonLet abforallnIfbconvergestheaconvergesIfadivergesthebdiverges
9、 = = = = 3.四种重要的级数1 23 11111: 1111 1(1) : ();123(2) : .|1, ;|1, ;1(3) : .n nnnnpnHarmonicseris divergencenGeometricserisaararararaIfrconvergencearIfrdivergencerFourserPseris Iis = =+ 61111 1(4) :()(0).lim 0, .: (| | | )nnnnnn nnnn nnAlternatingseris bIfbbandbconvergenceErorboundthenextermRSSa+=+ + +
10、 =4.幂级数和泰勒级数2 3012 30 ()2()(1) : .()(2) () )()()()() ().().;2! !()()() )()()()( . 0) ()!n nn nn n nn n n nnPowerseriscxccxcxcxcxTaylorseris fa fafxfafaxa xa xanLetfxPxRx faPxfafaxa xann oLa t= =+=+ + +=+=+ = (1)1()() ()( )(1)!n nn fgrangeerorboundRx xabetwenxandan + += +() ()202335 21123(3) 0) (0) 0)() (0)(0) . .! 2! !(4) :1 . .;2!3! !sin .(1) .;3!5! (21)!11 .1 n nn nn nx nnMacluriserisf f ffx xf fx x xn nFourseristoremberxx xexnxx xxx nxxxx= +=+ + +=+=+ +=+24 221.;cos1 .(1) .;2!4! (22)!n nnxxx xx n+=+ +
