数学分析数学分析数学分析 (25).pdf

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2、3f x yxy?)3,1(?)3,1(?)3,1(?)3,1(?13?)0,0(6?2?14533422422xyfxxyfyxy?00?0,1xy?=)0,0()1,1()1,1(?2122xxfx?2xyf?2122yyfy?224(61)(61)4Hxy?12.6.2?)1,1()1,1(?0H?xxf?)1,1()1,1(?2?)0,0(0H?(0,0)0f?22(,)2(2)f x xxx?4(,)2f xxx?)0,0()0,0(?3?202020 xyzfxfyfz?(0,0,0)(0,0,0)0f?2(,0)2f x yxy?2(0,0,)fz?z0)?(?(0,0,0)0,

3、0,0)?Hesse?H?()f xn?Rx?0 x()f x00()()()(TffH?xxxxxx?a?H?0()f x?b?H?0()f x?c?H?0()f x?Hesse?(,)f x y z(0,0,0)(,)f x y z 146?4?42242(32)020 xyfxxyxyfyxx?;0 xy?1,1xy?=?;1,82xy?=?3?)0,0(1,1)(1,1)?)83,22(?)83,22(?4230122xxfxyxy?324xyfxx?2yyf?422(30122)Hxyxy3 2(24)?xx?12.6.2?)83,22(?)83,22(?0H?xxf?)83,22(

4、?)83,22(?164?(1(1,1)(1,1)?0H?(1,1),1)?)0,0(0H?(0,0)0f?35(,)(1)2f x xxx?)0,0()0,0(?5?323200 xyafyxbfxy?22,abba&)$%(?332xxafx?1xyf?332yybfy?333341a bHx y?12.6.2?22,abba&)$%(?0H?xxf?147?),(22abba?3?ab?6?2221010120 xyzyfxzfxyfyz?1134242,2,2&)$%(?1134242,2,2&$%()?Hesse?314211124114220222022?&)?$?$?$%(?)2

5、,2,2(432141?144 22?2?0?xzxyzyxzyxf2223),(222?f?2220620420 xyzfxyzfyxfzx?(?Hesse?(0,0,0)0,0,0)222260204?&)$?$%(0,0,0)(0,0,0)0f?2211(,)(2)(2)22212f x y zxyxzy?(0,0,0)(0,0,0)0f?3.?yyyxyxfecos)e1(),(?(,)(1 e)sin0(,)e cos(1)e0yxyyyfx yxfx yxy?148?xk?,cos1yk?(,cos1)kk?0,1,2,k?=?(1)cosyxxfex?sinyxyfex?e co

6、s(2)eyyyyfxy?(,cos1)kk?cos(1)yyHke?e?k?0H?(,cos1)kk?k?0H?0 xxf?(,cos1kk)?4?)sin(sinsin),(yxyxyxf?2,0,0|),(?.?yxyxyxD?coscos()0coscos()0 xyfxxyfyxy?coscoscos()xyx?y?(,)|0,2x yx yxy?D?2xyxy?22,33?&$%()?0 x?0y?2xy?(,)0f x y?223 3(,)332f?0?233max?f?0min?f5?1,0bax?5?2xy?F?102)(),(dxybaJ5?1220(,)()J a bxa

7、xb dx?F2211(2)523aababb?Hesse?,a b21312&)$%(?1?3?,a b 149210322203abJabJab?11,6ab?11,6&?$%()?61?x5?6?R?123,?22123121sinsinsinsinsinsin()22RRS2?4?12233?2max433RS?7?R?H?h?213VR HR?2h?213VHhR?2222223VRhSRHR RhR Rh2R?R?h222222222032203SRRhhRhSVhRRhRRRh?I?I?I?I?52Rh?52Rh?213VR HR?2h?150?12Hh?215hHR?8?122

8、22?yxyx)(xyy?02?yxyxy,?,?0?yx12222?yxyx12?y)(xyy?1x?=1x?=?1y?21()1(12)2(2)yxyyyxyxyy?(1)y=)(xyy?1x?1?1x?1?22222()xxyyxyy?211?1y?)(xyy?1x?1?1x?1?9?08822222?zyzzyx),(yxzz?401284(2)0128zxxzyzyzyzyI?I?I?I?,?,?0?x02?zy08822222?zyzzyx0872?zz?81,7z?(,)zz x y?(0,2)?16(0,)7?151?2241 28zxzyI?I?20zx yI?I I?224

9、1 28zyzI?yI?(0,2)?16(0,)7?0H?(0,2)?1z?224015zxI?I?(0,2)?1z?16(0,)7?87z?224015zxI?I?16(0,)7?87z?1?2222(2)(1)(78xyzzz?)?(1)(78)0zz?.87z?1z.?2?1z?87z?10?Oxy?0?x?0?y?0162?yx?(,)x y?22216(,)()5xyD x yxy2?,x y22(216)542(216)0,5xyDxxyDyxy?0,?81,55xy?6?8 16(,)55?152?|(,)|lim(,)x yD x y?(,)D x y8 16(,)55?11?

10、1?2?2?cotcotcot()cotcottan()2S?2222cscsec()0,cscsec()0,SS?I?I?I?I?2?6?12?nn?1?nk?),2,1(nk?n)sin(sinsinsin21121121?nnS?11211coscos()02nkS?I?I?)1,2,1(?nk?1211212(nn)?1532kn?(1,2,kn)?n13?yx0,10?1e)1(?xyxy?)1(),(xyxyxfy?y?(1)(1ln)0yfxxyxyI?I?xyln1?)1,0(?xfyII?xyln1?(,)f x yy?xyln1?xexxln)1()(?)(x?21()(1

11、ln)lnxxxxexx?()1ln,(0,1)g xxxxx?()ln0g xx?(0)1,(1)0gg?()0g x?)(x?11lim()xxe?1(,)()f x yxe?(01,0)xy?14?xyxyx)3(?yyx)24(?0?22(3)(42)2234Pxy xxy yxxyyx?y?0,0,?,x y223244xyPxyPxy?15422223?x?222434?y?22223Pxxyyx?4y0222(2)(4)(2)4(2)0H?2xxP?Hesse?22223?x?222434?y?15512.6?1?8?xyxyx01368542y12244332?baxy?hol

12、d offx=0,1,3,6,8,5,4,2;y=1,2,2,4,4,3,3,2;plot(x,y,b*)hold on A=x,ones(size(x);B=y;x1=AB;a=x1(1);b=x1(2);y=a*x+b;plot(x,y,r)string=?y=,num2str(a),*x+,num2str(b);text(0.5,3.5,str,FontSize,16)?=0.37845+1.2531yx2?(%)x(%)yx16?517?518?519?520?521?522?523?524?5y43?542?641?840?640?338?737?236?034?0 156?hold

13、 offx=16.5,17.5,18.5,19.5,20.5,21.5,22.5,23.5,24.5;y=43.5,42.6,41.8,40.6,40.3,38.7,37.2,36.0,34.0;plot(x,y,b*)hold on A=x,ones(size(x);B=y;x1=AB;a=x1(1);b=x1(2);y=a*x+b;plot(x,y,r)str=?y=,num2str(a),*x+,num2str(b);text(18,44,str,FontSize,16)?=1.1483+62.9519yx?3?%?%?i12345678910?ix16.718.218.017.917.

14、416.617.217.715.717.1?iy17.518.718.618.518.217.518.018.216.917.8?yx?hold offx=16.7,18.2,18.0,17.9,17.4,16.6,17.2,17.7,15.7,17.1;y=17.5,18.7,18.6,18.5,18.2,17.5,18.0,18.2,16.9,17.8;plot(x,y,b*)hold on 157A=x,ones(size(x);B=y;x1=AB;a=x1(1);b=x1(2);y=a*x+b;plot(x,y,r)str=?y=,num2str(a),*x+,num2str(b);t

15、ext(15.6,18.5,str,FontSize,16)?=0.73979+5.2286yx4?16?xyx23456789y6.428.209.589.509.7010.009.939.99x1011121314151617y10.5010.5910.6010.6310.6010.9010.7610.80?cbxaxy?2?hold offx=2:17;y=6.42,8.20,9.58,9.50,9.70,10.00,9.93,9.99,10.50,10.59,10.60,10.63,10.60,10.90,10.76,10.80;plot(x,y,b*)A=x.2,x,ones(siz

16、e(x);a=Ayhold on y=a(1)*x.2+a(2)*x+a(3)plot(x,y,r)string=?y=,158num2str(a(1),*x2+,num2str(a(2),*x+,num2str(a(3);text(5,8,string)?20.0257460.688296.2507yxx?5?t?mt3691215182124m57.641.531.222.915.412.18.96.4?mtbtame?hold offx=3:3:24;y=57.6,41.5,31.2,22.9,15.4,12.1,8.9,6.4;plot(x,y,b*)hold on y1=log(y);A=x,ones(size(x);a=Ay1;y=exp(a(2)*exp(a(1)*x)?plot(x,y,r)string=?m=,num2str(exp(a(2),*e,num2str(a(1),*t;text(8,28,string,FontSize,16)?-0.10443tm=78.448e 159 160