微积分极限基本公式 微积分极限公式运算法则

乐乐今天给分享微积分极限基本公式的知识，其中也会对微积分极限公式运算法则进行解释，希望能解决你的问题，请看下面的文章阅读吧！

微积分极限基本公式 微积分极限公式运算法则

1、如果说是微积分常用公式，则应只包括极限、求导、不定积分、定积分、无穷级数，不包括三重积分、曲线曲面积分和场论。

2、应把《微积分》与《高等数学》、《数学分析》严格区分开，以免吓坏了经济类同学。

3、1.极限类：sinx/x→1 (x→0) (1+1/x)^x→2 (x→∞) "0/0型" f(x)/g(x)→f'(x)/g'(x)2.求导：(C)'=0 (x^a)'=a*x^(a-1) (a^x)'=a^xlna (e^x)'=e^x (logax)’=1/(xlna) (lnx)'=1/x(sinx)’=cosx (cosx)’=-sinx (tanx)’=sec2x (arcsinx)’=1/√(1-x2) (arccosx)’=-1/√(1-x2) (arctanx)'=1/(1+x^2)(u±v)'=u'±v' (uv)'=u'v+uv' (u/v)'=(u'v-uv')/v^2 dy/dx=1/(dx/dy) y=f(x) x=g(t) dy/dt=dy/dx*dx/dt3.微分：dy=f'(x)dx4.积分：基本：求导公式反过来，换元，分部：∫udv=uv-∫vdu ∫[a,b]f(x)dx=F(b)-F(a)5.级数：比较对象：几何、调和、p级数，|a(n+1)/a(n)|→L 收敛半径R=1/L你可以买本高数书啊，上面有Dx sin x=cos xcos x = -sin xtan x = sec2 xcot x = -csc2 xsec x = sec x tan xcsc x = -csc x cot xsin x dx = -cos x + Ccos x dx = sin x + Ctan x dx = ln |sec x | + Ccot x dx = ln |sin x | + Csec x dx = ln |sec x + tan x | + Ccsc x dx = ln |csc x - cot x | + Csin-1(-x) = -sin-1 xcos-1(-x) = - cos-1 xtan-1(-x) = -tan-1 xcot-1(-x) = - cot-1 xsec-1(-x) = - sec-1 xcsc-1(-x) = - csc-1 xDx sin-1 ()=cos-1 ()=tan-1 ()=cot-1 ()=sec-1 ()=csc-1 (x/a)=sin-1 x dx = x sin-1 x++Ccos-1 x dx = x cos-1 x-+Ctan-1 x dx = x tan-1 x- ln (1+x2)+Ccot-1 x dx = x cot-1 x+ ln (1+x2)+Csec-1 x dx = x sec-1 x- ln |x+|+Ccsc-1 x dx = x csc-1 x+ ln |x+|+Csinh-1 ()= ln (x+) xRcosh-1 ()=ln (x+) x≥1tanh-1 ()=ln () |x| 1sech-1()=ln(+)0≤x≤1csch-1 ()=ln(+) |x| >0Dx sinh x = cosh xcosh x = sinh xtanh x = sech2 xcoth x = -csch2 xsech x = -sech x tanh xcsch x = -csch x coth xsinh x dx = cosh x + Ccosh x dx = sinh x + Ctanh x dx = ln | cosh x |+ Ccoth x dx = ln | sinh x | + Csech x dx = -2tan-1 (e-x) + Ccsch x dx = 2 ln || + Cduv = udv + vduduv = uv = udv + vdu→ udv = uv - vducos2θ-sin2θ=cos2θcos2θ+ sin2θ=1cosh2θ-sinh2θ=1cosh2θ+sinh2θ=cosh2θDx sinh-1()=cosh-1()=tanh-1()=coth-1()=sech-1()=csch-1(x/a)=sinh-1 x dx = x sinh-1 x-+ Ccosh-1 x dx = x cosh-1 x-+ Ctanh-1 x dx = x tanh-1 x+ ln | 1-x2|+ Ccoth-1 x dx = x coth-1 x- ln | 1-x2|+ Csech-1 x dx = x sech-1 x- sin-1 x + Ccsch-1 x dx = x csch-1 x+ sinh-1 x + Csin 3θ=3sinθ-4sin3θcos3θ=4cos3θ-3cosθ→sin3θ= (3sinθ-sin3θ)→cos3θ= (3cosθ+cos3θ)sin x = cos x =sinh x = cosh x =正弦定理:= ==2R余弦定理: a2=b2+c2-2bc cosαb2=a2+c2-2ac cosβc2=a2+b2-2ab cosγsin (α±β)=sin α cos β ± cos α sin βcos (α±β)=cos α cos β sin α sin β2 sin α cos β = sin (α+β) + sin (α-β)2 cos α sin β = sin (α+β) - sin (α-β)2 cos α cos β = cos (α-β) + cos (α+β)2 sin α sin β = cos (α-β) - cos (α+β)sin α + sin β = 2 sin (α+β) cos (α-β)sin α - sin β = 2 cos (α+β) sin (α-β)cos α + cos β = 2 cos (α+β) cos (α-β)cos α - cos β = -2 sin (α+β) sin (α-β)tan (α±β)=, cot (α±β)=ex=1+x+++…++ …sin x = x-+-+…++ …cos x = 1-+-+++ln (1+x) = x-+-+++tan-1 x = x-+-+++(1+x)r =1+rx+x2+x3+ -1= n= n (n+1)= n (n+1)(2n+1)= [ n (n+1)]2Γ(x) = x-1e-t dt = 22x-1dt = x-1 dtβ(m, n) =m-1(1-x)n-1 dx=22m-1x cos2n-1x dx = dx。

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