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1、高等数学II实验参考答案唐诗权编写第5章1.（1）>>symsxy;>>f=(1-cos(x^2+y^2))/((x^2+y^2)*exp(x^2*y^2));>>limit(limit(f,x,0),y,0)ans=0（2）>>symsxy;>>f=(log(x*exp(x)+exp(y)))/sqrt(x^2+y^2);>>limit(limit(f,x,0),y,0)ans=NaN（3）>>symsxy;>>f=(2*x*sin(y))/(sqrt(x*y+1)-1);>>limit(limit(f,x,0),y,0)ans=42.（1）syms
2、xy;z=((x^2+y^2)/(x^2-y^2))*exp(x*y);zx=diff(z,'x')zx=(2*x*exp(x*y))/(x^2-y^2)-(2*x*exp(x*y)*(x^2+y^2))/(x^2-y^2)^2+(y*exp(x*y)*(x^2+y^2))/(x^2-y^2)zy=diff(z,'y')zy=(2*y*exp(x*y))/(x^2-y^2)+(x*exp(x*y)*(x^2+y^2))/(x^2-y^2)+(2*y*exp(x*y)*(x^2+y^2))/(x^2-y^2)^2（2）symsxyz;u=log(3*x-
3、2*y+z);ux=diff(u,'x')ux=3/(3*x-2*y+z)uy=diff(u,'y')uy=-2/(3*x-2*y+z)uz=diff(u,'z')uz=1/(3*x-2*y+z)（3）symsxy;z=sqrt(x)*sin(y/x);zx=diff(z,'x')zx=sin(y/x)/(2*x^(1/2))-(y*cos(y/x))/x^(3/2)zy=diff(z,'y')zy=cos(y/x)/x^(1/2)（4）symsxy;z=asin(y*sqrt(x));zx=diff(z,'x')zx=y/(2*x^(1/2)*(1-
4、x*y^2)^(1/2))zy=diff(z,'y')zy=x^(1/2)/(1-x*y^2)^(1/2)3.symsxy;f=x+y-sqrt(x^2+y^2);fx=diff(f,'x');fy=diff(f,'y');x=2;y=4;fx0=subs(fx)fx0=0.5528fy0=subs(fy)fy0=0.10564.symsxyza;f=x^2+y^2+z^2-2*a*x*y*z;fx=diff(f,'x');fy=diff(f,'y');fz=diff(f,'z');dzx=-fx/fzdzx=-(2*x-2*a*y*z)/(2*z-2
5、*a*x*y)dzy=-fy/fzdzy=-(2*y-2*a*x*z)/(2*z-2*a*x*y)5.symsxyuvRduxdvxduydvy;f=x^2+y^2+u^2+v^2-R^2;g=x+y+u+v;fx=diff(f,'x');fy=diff(f,'y');fu=diff(f,'u');fv=diff(f,'v');gx=diff(g,'x');gy=diff(g,'y');gu=diff(g,'u');gv=diff(g,'v');ffx=fu*dux+fv*dvx+fx;ggx=gu*dux+gv*dvx+gx;[dux,dvx]=so
6、lve(ffx,ggx,'dux','dvx')dux=(v-x)/(u-v)dvx=-(u-x)/(u-v)ffy=fu*duy+fv*dvy+fy;ggy=gu*duy+gv*dvy+gy;[duy,dvy]=solve(ffy,ggy,'duy','dvy')duy=(v-y)/(u-v)dvy=-(u-y)/(u-v)6.symsxyz;f=x+y+z-exp(-(x+y+z));fx=diff(f,'x');fz=diff(f,'z');dzx=-fx/fz;g=dzx;gy=diff(g,'y');gz=diff(g,'z');dzxy=g
7、y+gz*dzxdzxy=07.symsxy;z=x^2-x*y-2*y^2;zx=diff(z,'x');zy=diff(z,'y');fzx=inline(zx);fzy=inline(zy);a=pi/3;b=pi/6;f1=fzx(1,2)*cos(a)+fzy(1,2)*cos(b)f1=-7.79428.symst;x=sin(t);y=cos(t);z=t;dx=diff(x,'t');dy=diff(y,'t');dz=diff(z,'t');x1=inline(dx);x2=inline(dy);x3=inline(dz);t=pi/
8、4;a=sin(t);b=cos(t);c=t;x10=x1(a)x10=0.7602x20=
