AP微积分BC公式大全.pdf

1 APAPAPAP微积分公式大全微积分公式大全 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 Chapter1 Chapter1 Chapter1 FunctionFunctionFunctionFunction andandandand L L L Limitimitimitimit 1 5种基本初等函数图像性质 111111 log sin cos tan cot sec csc sin cos tan cot sec csc x a Power yxExponential yaLogarithmic yx Trigonometric yxxxxxx Inversetrigonometricyxxxxxx 2 4种表达函数的解析式 xf t yf xparametricpolar rfvector r tf tg t yg t 3 3个重要极限 0 sin lim1 x x x 1 0 1 lim 1 lim 1 x x xx exe x 0 0 1 011 1 011 limlim 0 mm mmm nn xx nnn a nm b P xa xa xaxa nm Q xb xb xbxb nm Chapter2 Chapter2 Chapter2 Chapter2 DerivativesDerivativesDerivativesDerivatives 2 1 导数定义式 0 0 00 0 00 000 0 0 0 000 0 0 0 1 limlim 2 limlim limlim xx xxx xxx f xxf xy fx xx f xf xf xxf x Oneside fx xxx f xf xf xxf x fx xxx 2 求导公式和法则 1 2 2 2 1 111 2 11 ln log ln ln sin cos cos sin tan sec cot csc sec sec t nn xxxx a Derivative formulas of fivebasic elementry functions xnxx xxx aaaeexx xax xxxxxx xxxx 2 22 2 22 2 an csc csc cot 111 arcsin arccos arctan 1 11 111 cot sec cot 1 1 1 2 3 xxxx xxx x xx arcxarcxarcx x xxxx uu vuv Operationuvuvuvu vuv vv Chain rule 2 2 4 1 5 sin cossin yf g x dydy du dxdu dx Logarithmic differentiation dy Inverse function dxdx dy dydy dtd yd dy dxdt parametric dxdx dtdxdx dt dyfrcos polarvector r tftg t dxfr Chapter3 Chapter3 Chapter3 Chapter3 IntegralIntegralIntegralIntegral 3 1 不定积分定义式 definition fx dxf xCmethod df xf xC 2 求不定积分的四种方法 1 121 2 2 1 1 1ln sincos cossin tanln cos cotln sin secln sec tan cscln csc cot sin 1 tan 1 1 n nuu x Formulasx dxCa duaC na xdxxCxdxxCxdxxC xdxxCxdxxxCxdxxxC dxdxdx xC xxC x xx 3 反常积分的两种形式 1 lim lim 2 lim lim b aab bb aa bb ac ca a cb Integral on an Infinite Interval f x dxf x dx f x dxf x dx f x dxf x dxf x dx Integrand with Infinite discontinuities f x dxf x dx f x dx bc a bcb aac f x dx f x dxf x dxf x dx 4 定积分定义和运算法则 1 2 limlim 3 b ii ann Riemann sum left right mid trapezoidal definitionf x dxAf xx properties of Integral 4 bbb aaa bb aa f xg x dxf x dxg x dx kf x dxkf x dx 0 0 0 2 bcb aac aab aba aaa aa f x dxf x dxf x dx f x dxf x dxf x dx f x dxf x oddf x dxf x dx f x even 5 微积分两条基础理论 bb aa x a fx dxf bf a or f bf afx dx dA xd f t dtf x xa b dxdx 6 定积分应用 22 11 22 22 1 2 3 sec 4 1 1 b a xy xy f x dx Mean value theorem f c ba Area vertical slice horizontal slice polar Volume disk washer shell known crosstion dydx Length of curve Ldxdy dxdy or Lxtyt dtparametric equation 7 微分方程 1 2 1 lim 1 kx t dy SeparationVariableM x dx N y dyyK Logistic equationkyy Differenti andyK dxKA al equation e 11000 3 4 nnn Slope field Eluer s method yyh yor f xf xfxxx 5 Chapter4 Chapter4 Chapter4 Chapter4 SeriesSeriesSeriesSeries 1 级数的定义与收敛性 123 1 123 1 1 1 1 2 3 lim lim nn n n nnn n nn n n nn n n aaaaa partial sum Saaaaa IfS exits thena converges IfS does not exit thena diverges Definition 2 判定级数收敛性的三大审敛法 1 1 1 1 1 lim 1 1 1 2 1 n n n n n n n n a Ratioa a convergencedivergencemay convergence or divergence Integral If af n is positive continuous and decreaing for x thenaandf x dx both converg Threete nce s e t 11 11 3 0 nn nn nn nn nn or divergerence Comparison Letab for all n Ifbconverges thena converges Ifa diverges thenb diverges 3 四种重要的级数 1 231 1 1 1 1 11111 1 123 2 1 1 1 1 3 n n n n n p n Harmonic seriesdivergence nn Geometric series aarararar a If rconvergencearIf rdivergence r Four ser PseriesI n ies 6 1 1 1 11 4 1 0 lim0 n nn n nnn n nnnn Alternating seriesb b If bbandbconvergence Error bound the next term RSSa 4 幂级数和泰勒级数 23 0123 0 2 1 2 2 0 nn nn n n n nn n n n Power series c xcc xc xc xc x Taylor series fafa f xf afa xaxaxa n Let f xP xR x fa P xf afa xaxa n n o La t 1 1 1 n n n f grange error bound R xxabetween x and