2019考研高昆仑数学零基础高数第13章讲义

1、1.1xy, D,yxD,yfyx,yf x.x,y, D.:1:.,.1, x0, x1, x0002yf gx yg x0yxyyfx0xyttFx, y0.2.12fyfxX,M ,xX ,f xM ,xX.:1,sin, arctan x2223M ,x1X ,f x1M ,f xX.1 / 112yf xf x2I,Ix2,1fx1fx1f x2,fxI.34fyf xD.,xD,xffxx,fx ,xDx,f,fD.:1,2,sin3y,f,x0,00.45fT ,fx,fx+Tfx,x,T,sinx.:.3.6yf xD,x ,Rf ,xfyxRf ,1xD,yfyyf.: 11

2、12yfx,x, fyfx, yf xyfx1y1xy1fxxx.fy3ffxfx4.7yygfxuDf ,uug xug xDg ,RgDf ,fyf.2 / 115.8,.:;.1, x0, x1, x11 , g1ex ,2f xxfgxgfx,.n 110,N ,na.N,xna.axn.nlim xna,nxn:xna,12.nn1xna,.230,0,NNN ,N ,nnNN,xn ,axnac;xnc,.3 / 113Nlim xna,a0a0 ,N ,nn,xn0xn0 .nnnnnx0Ux0,Ux0;oUUx0x0 ,00,0oUx0,x0 ,.1fxx0,0,0,f xfx

3、,0aaf,lim fx x0xA.00x0limlimf xlim f0x.1lim fxAfxlim0f xA.x1, x01f0fx.x1, x0x4 / 11xlim fxlim fxf xA.xlim f xx.xAlimfxlim0x x003lim fxx x00 .a,a0a0 ,0,004lim fx x0x, xnxnfx0 ,flim fnxnlim fx x0x.,1ffx,0x.00:123.2f,M,0X0 ,0Xx,f xf xM ,fx.05 / 112(:,fx,1x1;,fx,fx0,.ffx1y1(ff:lim f xlim f xA, lim gxB,l

4、imlimxxg xg xlim flim glim gxABBlim f xlim gxAxxfgxxABlimB0 .:1.,lim g,x;,.1lim fx,x,lim0lim f0lim0fgx2lim fxlim g xxgx,3lim fx, lim gxfxgx,4lim fxlim gx,lim0fxgx.x312lim.2x 2 x5x 3200231limx 3.3223xx12(g x:yf,g xlim gx x0yu0 ,f uyuf ugxu,fx0xu0lim fg xflim gx0xfu0.x3 .5limx 3x296 / 111.12:xn0, yn ,

5、 zn:Na.,nN,xnynzn,lim xnlim znnnynlim yna.n:nnnnnnx1x03sin xx01.lim0, lim0,0lim0,o2lim,3limc0,limc0,kk5lim1,.7 / 11:123,.222232235235222.1111:x0,ex2 ,sinarctan xln 1+x11 x, ax1x1x ln a .sin x2lim.0 x33xx1 tan x1sin x .3limx 0tan xsin x3x 0lim ln cos x .5x22xx 03x6A fC ffxx2,x0, .B f xD f xxxxxx8 / 1

6、11limyx 02lim f (x)x x03yfx0 yf (x)xf (x)f (x)x0x0x0x0,x0,limx 0f0,f (x).f (x0 ),.lim f (x)0f (x0 ),f (x0 ),f (x)x0x0.limf (x)f (x).x0+x4f (x)f (x)a, ba, b,f (x)a, b.f (x)xaxba, b,.yxf (x)x0x0f (x):,12xx0x0limx x0limf (x),3x,f (x),lim0.f (x)fx0 .f (fx0.cosa,1fxx0,a .20x9 / 111ex1,2f xx0fx.1ex1BACD2n

7、n1.fx , g xx0,fgxxfxg xfxgxgx0x.002.ugxx0f, yfx0uu0gx0, ygx.3.xy.1fxR,fx0,x,2R,.1fx2xxf x3fx4.ex ,axx, x002fx,afx,.10 / 112fxa, bbxy,fxa, bf,yfL x0.y ,L,faf0.:3:f xf,a, b,lim fxx,ff x,x,.:x,lim fx axlimx b,fxa, b.ab.11 / 11fx01: f.00000h0xx00fx0xfx02 :fx0lim.002 x3, x312fx,fxx1 .x2 ,x1ACBD,fx0hf x0h

8、31fx,limh 00hafahfah2limh 0,f2hx2 ,x14fx,fxx1a, b,.axb, x11yf xx0f xfx0M x0 , fyfxM x0 , f x0yx0: yf x0f.0:5f xf xf x,f0,: f,0f0.xa, aa, aT,fxT.6f xf xx5x0f1sin x.3 f1sin x8xox,1yfx6, f6u, vv,uuvuvu vuvuvu vuvv0.v2ydx dyf (x)f(x)0,xy,1dydx1(x),y.fdydxdydu ,yf (u), ug(x),yfg(x),dudxyfugxfg xgx.11y:ln

9、lnx2yfx,f x, fx0.2xx13xx242y.s4fx.000006fx,Fxfx1+ sin x,fB D00F xx0 .ACyfxfxx,fxyfx,d 2 y dx2, yfd 2 ydx2d dxxdydxy,yy.xnfn 1.1.2.n2n2nnneax baneax b ;sinaxban sinaxb,cosaxban cosaxb;nn1 !1n!n1 n 1 an1 n anln(axb),.nn 1axbaxbaxb3.3d 2 xdxdy1yy13 .:dy2y22022 xtt22xya cos tb sin t4t.41:Ayfxx0xfyx0fdy,

10、yA xo,x ,0A x.A xfdy,0000x x000x x004yfxx0ydyfx0 dxyfxx0 , f x0f xx0 , f x0x0y.1: 1f x2duu2y0.02.e1 3x cos x,3ydy.4d,.1xdx2dcostdt.5f xU x0x0fUx0x0,x0x0f,0.x,xff xf,x0fx1,a,b2a,b,3fafb,a,bf0.a xna xn 1a nxn 1xn 22an 13a,an 101n 10010x0a,b.f x1, x3xx,0.fx1fx2f x3,ab,3:f,4f0, a,0, a,fa0,0, aff0.:,fx1a

11、,b,2a, ba, bfbfafba.fxI, I0f xI.6lim fxxk,limxf xafx.1200n2nn0000000002nn01020n00n0000102n0nn 12nn 1000000000x00,x23333244233221f xtan x3.3x 0x2cos xe 23limx 0.32n5fx0nf0n3 .1:ffIxI,Ifx0fx0 ,x.:0.21f12x3.22224ln xaxa01:f (x)a, b,22f (,f (x)a, b.220000044:f.012ff0 , f x00 , fx0.5:x0 , fx0 , ffx x0x0x0,fx00.12ffx0x00,0,.y3x44x351.2x26yk3k,.71f xt x1tx2a,b1fx2x0,a,bx1, x20t1,ftfx1tf.1:f (x0,fxfx0f xffx0,fx0fx.;x2:f.01ffxf,0, x0,fx, x02.03:fxx0,fx00.1ffx0fx00,0, x00,x0,fx00, x02x0x0,.235n 1n3fnxx0n,fx x0,fx0fx0fx00, fx00.:1nx0n2,fx,fx00