高等数学基础知识点大全

[e-mail]1/[e-mail]……abc……aAaAaAaAaANN+N+ZQRABABABABABBAABBAABABABABBAABAAABCABBCACABABABABx|xAxBABABABABx|xAxBU2/[e-mail]|xUxAcardAa,b,ccard(A)=3ABcard(A)+card(B)=card(AB)+card(AB)1Ax|xBx|xCx|xABAB2C{(x,y)|y=x}yxD={(x,y)|2x-y=1,x+4y=5}CD3A={x|1x3}B{x|(x-1)(x-a)=0}BAaAB4ABC5A1234nB24682nab[ab]ababb][a3/[e-mail][a(-b)(-,0.x-yy=f(x)y=F(x)fFa)x2+y2=r2b)c)If(x)f(x)Icosx(-,+.(a,b)(a,b)x1x2x1x2(a,b)4/[e-mail](a,b)(a,b)x1x2x1x2(a,b)=x2(-,0)(0,+==-lltgxy0x0.(ab)RR).)y=x2(-,+[0,+).x=±.(-,+5/[e-mail]=y=x2).y=xy=x(-,+6/[e-mail]):,y;b):x=0,y=1.a):(1,0)b):(0,1)(-,+.a=m/na):,y;b):m,n,y;c):,y(-,0).)a):b):)a):[-/2,/2],..)7/[e-mail]):(-,+b)c)a):(-,+b)c)(0,1)a):(-,+b)c)y=1y=-1shxthxchxsinxtanxcosx.8/[e-mail])(-,+b)[1,+c)(-1,+1)a1a2ana1a2an.an.ananA1A2A36×2n-1AnA1A2A3AnAnA1A2A3An…)a.(a-a+9/[e-mail](a-a+1-1-1(-1)n+1…1.a)b)x0?!)a):10/[e-mail]):.x=1,:2.x0x0x0x=x0Aa):11/[e-mail]):c):d):10x0.12/[e-mail],x(xx0x0(xx0x0x0x0x0x0x)A..13/[e-mail]=2.718281828459045.....x=-2t1/x0.y=x=x0Ny=NM14/[e-mail].)00.a)b)c).x0a)b)c))3xx23xsinx15/[e-mail]2.————x1x2x2-x1x=x2-x1.x0x0x0+x16/[e-mail]0x0x0x0.(a,b]b[a,b)a.(a,b)(a,b)[ab]..a)x0b)x0c)x017/[e-mail]=0-1+1x=0x=0x=0:x0x0.x0x0x0x018/[e-mail])b)c)[-1,1]x0u=ax0u=ex=x0u=u0x=x0.19/[e-mail])y=sinx[0x=/2[0]x=3/2-1[0[ab]xxtt0t0t0t0t0t0=x0x0x(x+x0x0x0(a,b)(a,b)(a,b)20/[e-mail]=x0x=x0x0x0).21/[e-mail]!=??2x22/[e-mail]...23/[e-mail](t)s(t)(n-1).=a=024/[e-mail]=sinxy=1+3x.F(x,y)=0F(x,y)=0y.F(x,y)=0a)F(x,y)=0b)F(x,y)=0=x=0x=0y=0.25/[e-mail]0x0x026/[e-mail],27/[e-mail]2x+1———)28/[e-mail]3.1.025(1.024695)29/[e-mail](ab)(a,b)(a,b)ABABP(x=c)[a,b](a,b)(a,b)[a,b](a,b)(a,b)1730/[e-mail]——[ab](ab)(ab)[01](0,1)a(31/[e-mail](L'Hospital)(L'Hospital)a(N)=(L'Hospital)32/[e-mail]33/[e-mail]),)..[a,b](a,b).a)(a,b)[a,b]b)(a,b)[a,b]..)(0,(-,0)x=1x=2x=1x=1.34/[e-mail]=1x(x=1x=2),——(a,b)x0(a,b).x0x(x0x0x(x0.——x0.x0x0x0x0x0x0x0a)35/[e-mail])——c)x=-2-4/5x0.a)x0b)x0c)=0.36/[e-mail][a,b](a,b)[-33/2]x=±137/[e-mail](a,b)(a,b)(a,b)38/[e-mail](a,b)[a,b](a,b)[a,b](0,+(a,b)(1)(2)=0(a,b)(3)(2)x0x0=0x=02/339/[e-mail]2/3f(x)F(x)dF'(x)=f(x)dxF(x)f(x)sinxcosxf(x)F(x)f(x)F(x)=f(x)F(x)+C(Cf(x)f(x).f(x)f(x)F(x)f(x)f(x)F(x)+C.:=F(x)+C40/[e-mail].=12f(u)F(u)u=g(x)F[g(x)]f[g(x)]g'(x).:u=2xcos2x=cosudu=2dxx=g(t)g'(t)f[g(t)]g'(t)(t)[g(x)]f(x).(g(x)x=g(t):.x=asint(-/2t/2)dx=acostdt,41/[e-mail]=u(x)v=v(x)(uv)'=u'v+uv'uv'=(uv)'-u'vu=xdv=cosxdxdu=dxv=sinxdvdv(1)v(2)42/[e-mail]=tan(x/2)x=u2+1dx=2udu43/[e-mail]———y=f(x)x=ax=bA.f(x)[a,b][a,b][a,b]f(x)[a,b][a,b]a=x0x1...xn-1xn=b[a,b][x0x1...[xn-1,xn],[xi-1,xii(xi-1xi),f(i)f(i)xi[a,b]Sf(x)[a,b]f(x)f(x)[a,b]f(x)[a,b]f(x)[a,b]f(x)[a,b]44/[e-mail](1).(2).(3)[a,b]f(x)g(x)ab)(4)f(x)[a,b]m(b-a)M(b-a)(5)f(x)[a,b][a,b]=f()(b-a)f(x)[a,b][a,b]f(x)[a,x]f(x)[a,x][a,b][a,b](x):(1)f(x)[a,b][a,b]b)(2)f(x)[a,b]f(x)[a,b]--45/[e-mail](3)F(x)f(x)[a,b][a,b][a,b]--f(x)[a,b]g(t)[m,n][m,n]x=g(t)[a,b]g(m)=a,g(n)=b:::x=asint,dx=acostdt,x=0t=0x=at=/2.46/[e-mail](x)v(x)[a,b]u'(x)v'(x)(uv)'=u'v+uv',[a,b]x=0t=0x=1t=1.u=t,dv=etdt,du=dt,v=et———f(x)[a,+ba.f(x)[a,+=.47/[e-mail](x)(-b]ab.f(x)(-b]=.f(x)(-,+=f(x)(a,b]0f(x)(a,b]48/[e-mail]..f(x)[a,b)0f(x)[a,b]c(acb)=+.(a0)x=a49/[e-mail](/2xz.x,y,z.x,y,zx,yx,y,zM(x,y,z).x,y,z50/[e-mail]=0zOxy=0y=z=0x=y=z=0M1(x1,y1,z1M2(x2,y2,z2A(4,3,1),B(7,1,2),C(5,2,3)ABC.ABCP1P2Ox,Oy,Oz,0,0.51/[e-mail]{AC}.52/[e-mail]1L2L1L2.L1L2L1L253/[e-mail](x0,y0,z0),{A,B,C}A2+B2+C2n{3-48}(2,1,-4).Ax+By+Cz+D=0.x,y,zAx+By+Cz=0.By+Cz+D=0.Ax+Cz+D=0.Ax+By+D=0.54/[e-mail]+Cz=0.Ax+Cz=0Ax+By=0.Ax+D=0By+D=0Cz+D=0.{l,m,n}Po(x0,y0,z0),55/[e-mail](x,y,z)x,y,z56/[e-mail],h`z=f(x,y).D57/[e-mail](.,y0.xOyz=f(x,y)M(x,y)xOyMP,(x,y)z=f(x,y)xOyz=f(x,y)yxOy(x,y)(x,y)f(x,y)f(x,y)(x,y)58/[e-mail](x,y)(x,y)f(x,y)(x,y)x,y)f(x,y)g(x,y)B.(1)f(x,y)±g(x,y)A±B(2)f(x,y).g(x,y)A.(3)f(x,y)/g(x,y)A/B0(x,y)(x0,y0f(x,y)f(x,y)(x0,y0f(x0,y0f(x,y)(x0,y0f(x,y)z=f(x,y)(x0,y0(x0,y0f(x,y)59/[e-mail]=0y=0xOy(x0,y0f(x,y)f(x,y)(x0,y0(x,y)f(x,y)z=f(x,y)(x0,y0y0x0z=f(x,y))xz=f(x0x)-f(x0,y0).xz=f(x,y)(x0,y0f'x(x0,y0z=f(x,y)(x0,y0y0z=f(x,y0x0x0y,60/[e-mail]=(x,y)(x0,y0.f'y(x0,y0z=f(x,y)(x0,y0f'x(x0,y0f'y(x0,y0f(x,y)(x0,y0f(x,y)f(x,y)D(x,y)x(y)f(x,y)x(y)z=x2siny..61/[e-mail].z=f(x,y)f'x(x,y)f'y(x,y)z=f(x,y)fxxfxyfyxfyy.fxyfyx.fxyfyx.z=f(x,y)f'x(x,y),f'y(x,y)x,f'x(x,y)x+f'y(x,y)y()z=f(x,y)(x,y)x,y