restart;f:=(x,y)->exp(x)*sin(x+y);

NiM+SSJmRzYiZio2JEkieEdGJUkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSRleHBHRiU2IzkkIiIiLUkkc2luR0YlNiMsJkYxRjI5JUYyRjJGJUYlRiU=

x0:=0.5;y0:=0.5;

NiM+SSN4MEc2IiQiIiYhIiI=

NiM+SSN5MEc2IiQiIiYhIiI=

z:=(x,y)->D[1](f)(x0,y0)*(x-x0)+D[2](f)(x0,y0)*(y-y0)+f(x0,y0);

NiM+SSJ6RzYiZio2JEkieEdGJUkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgqJi0tJkkiREdGJTYjIiIiNiNJImZHRiU2JEkjeDBHRiVJI3kwR0YlRjQsJjkkRjRGOCEiIkY0RjQqJi0tJkYyNiMiIiNGNUY3RjQsJjklRjRGOUY8RjRGNC1GNkY3RjRGJUYlRiU=

z(x,y);

NiMsKEkieEc2IiQiKzshZiJ5QSEiKiQhKltCOCg+RigiIiJJInlHRiUkIitYIXohMyopISM1

Zapprox:=z(0.55,0.55);

NiM+SShaYXBwcm94RzYiJCIrZSUqelg6ISIq

Zgenau:=f(0.55,0.55);

NiM+SSdaZ2VuYXVHNiIkIitaeW9XOiEiKg==

absoluterFehler:=abs(Zgenau-Zapprox);

NiM+STBhYnNvbHV0ZXJGZWhsZXJHNiIkIig2OzYiISIq

relativerFehler:=absoluterFehler/Zgenau;

NiM+STByZWxhdGl2ZXJGZWhsZXJHNiIkIitmck0nPighIzg=

restart;f:=(x,y)->3*x*y**2+4*x**3-3*y**2-12*x**2+1;

NiM+SSJmRzYiZio2JEkieEdGJUkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCwqJjkkIiIiOSUiIiMiIiQqJEYvRjMiIiUqJEYxRjIhIiQqJEYvRjIhIzdGMEYwRiVGJUYl

fx:=D[1](f);

NiM+SSNmeEc2ImYqNiRJInhHRiVJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwoKiQ5JSIiIyIiJCokOSRGMCIjN0YzISNDRiVGJUYl

fy:=D[2](f);

NiM+SSNmeUc2ImYqNiRJInhHRiVJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmKiY5JCIiIjklRjAiIidGMSEiJ0YlRiVGJQ==

solve({fx(x,y)=0,fy(x,y)=0},{x,y});

NiY8JC9JInlHNiIiIiEvSSJ4R0YmRic8JEYkL0YpIiIjPCQvRikiIiIvRiVGLDwkRi4vRiUhIiM=

Delta:=(x0,y0)->D[1](fx)(x0,y0)*D[2](fy)(x0,y0)-D[2](fx)(x0,y0)**2;

NiM+SSZEZWx0YUc2ImYqNiRJI3gwR0YlSSN5MEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJi0tJkkiREc2JEkqcHJvdGVjdGVkR0Y0SShfc3lzbGliR0YlNiMiIiI2I0kjZnhHRiU2JDkkOSVGNy0tJkYyNiMiIiM2I0kjZnlHRiVGOkY3RjcqJC0tRj9GOEY6RkEhIiJGJUYlRiU=

Delta(0,0);

NiMiJFci

D[1](fx)(0,0);

NiMhI0M=

Delta(2,0);

NiMiJFci

D[1](fx)(2,0);

NiMiI0M=

Delta(1,2);

NiMhJFci

Delta(1,-2);

NiMhJFci

P(0,0) -> lokales MaximumP(2,0) -> lokales Minimumplot3d(f(x,y),x=-100..100,y=-100..100);

-%'PLOT3DG6%-%%GRIDG6%;$!$+"""!$"$+"F+F(X,I)anythingGI*protectedGF06"F1[gl'!%"!!#\bm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xF1Q"yF1Q!F1-%%FONTG6$%*HELVETICAG"#5

=> alles lokale Extremwerte

restart;u:=(s,t)->s*t-27*(1/s-1/t);

NiM+SSJ1RzYiZio2JEkic0dGJUkidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgqJjkkIiIiOSVGMEYwKiRGLyEiIiEjRiokRjFGMyIjRkYlRiVGJQ==

us:=D[1](u);

NiM+SSN1c0c2ImYqNiRJInNHRiVJInRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSUiIiIqJDkkISIjIiNGRiVGJUYl

ut:=D[2](u);

NiM+SSN1dEc2ImYqNiRJInNHRiVJInRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSQiIiIqJDklISIjISNGRiVGJUYl

solve({us(s,t)=0,ut(s,t)=0},{s,t});

NiQ8JC9JInRHNiIhIiQvSSJzR0YmIiIkPCQvRiUsJC1JJ1Jvb3RPZkc2JEkqcHJvdGVjdGVkR0YxSShfc3lzbGliR0YmNiQsKCIiIkY1SSNfWkdGJiEiIiokRjYiIiNGNS9JJmxhYmVsR0YwSSRfTDFHRiZGKi9GKSwkRi5GJw==

evalf(%);

NiQ8JC9JInRHNiIkISIkIiIhL0kic0dGJiQiIiRGKTwkL0YrXiQkISsrKysrOiEiKiQhKzZpMilmI0YzL0YlXiQkIisrKysrOkYzJCIrNmkyKWYjRjM=

fsolve({us(s,t)=0,ut(s,t)=0},{s,t});

NiM8JC9JInNHNiIkIisrKysrSSEiKi9JInRHRiYkISsrKysrSUYp

Delta:=(s0,t0)->D[1](us)(s0,t0)*D[2](ut)(s0,t0)-D[2](us)(s0,t0)**2;

NiM+SSZEZWx0YUc2ImYqNiRJI3MwR0YlSSN0MEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJi0tJkkiREc2JEkqcHJvdGVjdGVkR0Y0SShfc3lzbGliR0YlNiMiIiI2I0kjdXNHRiU2JDkkOSVGNy0tJkYyNiMiIiM2I0kjdXRHRiVGOkY3RjcqJC0tRj9GOEY6RkEhIiJGJUYlRiU=

Delta(3,-3);

NiMiIiQ=

D[1](us)(3,-3);

NiMhIiM=

P(3,-3) -> lokales Maximumplot3d(u(x,y),x=-5..5,y=-5..5);

-%'PLOT3DG6%-%%GRIDG6%;$!"&""!$""&F+F(X,I)anythingGI*protectedGF06"F1[gl'!%"!!#\bm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30C30C40335DDDDDDDDDDD40348CCCCCCCCCCC4035E9D0369D036940376856E2856E284039000000000000-%+AXESLABELSG6%Q"xF1Q"yF1Q!F1-%%FONTG6$%*HELVETICAG"#5

=> lokale Extremwerte

restart;h:=(x,y)->(x**2+y**2)*exp(-x);

NiM+SSJoRzYiZio2JEkieEdGJUkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsJiokOSQiIiMiIiIqJDklRjFGMkYyLUkkZXhwR0YlNiMsJEYwISIiRjJGJUYlRiU=

hx:=D[1](h);

NiM+SSNoeEc2ImYqNiRJInhHRiVJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmKiY5JCIiIi1JJGV4cEc2JEkqcHJvdGVjdGVkR0Y0SShfc3lzbGliR0YlNiMsJEYvISIiRjAiIiMqJiwmKiRGL0Y5RjAqJDklRjlGMEYwRjFGMEY4RiVGJUYl

hy:=D[2](h);

NiM+SSNoeUc2ImYqNiRJInhHRiVJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwkKiY5JSIiIi1JJGV4cEc2JEkqcHJvdGVjdGVkR0Y0SShfc3lzbGliR0YlNiMsJDkkISIiRjAiIiNGJUYlRiU=

solve({hx(x,y)=0,hy(x,y)=0},{x,y});

NiQ8JC9JInlHNiIiIiEvSSJ4R0YmRic8JEYkL0YpIiIj

Delta:=(x0,y0)->D[1](hx)(x0,y0)*D[2](hy)(x0,y0)-D[2](hx)(x0,y0)**2;

NiM+SSZEZWx0YUc2ImYqNiRJI3gwR0YlSSN5MEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJi0tJkkiREc2JEkqcHJvdGVjdGVkR0Y0SShfc3lzbGliR0YlNiMiIiI2I0kjaHhHRiU2JDkkOSVGNy0tJkYyNiMiIiM2I0kjaHlHRiVGOkY3RjcqJC0tRj9GOEY6RkEhIiJGJUYlRiU=

Delta(0,0);

NiMiIiU=

D[1](hx)(0,0);

NiMiIiM=

evalf(Delta(2,0));

NiMkIStfYkRFdCEjNg==

P(0,0) -> lokales Minimumplot3d(h(x,y),x=-10..10,y=-10..10);

-%'PLOT3DG6%-%%GRIDG6%;$!#5""!$"#5F+F(X,I)anythingGI*protectedGF06"F1[gl'!%"!!#\bm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xF1Q"yF1Q!F1-%%FONTG6$%*HELVETICAGF-

=> lokale Extremwerte

restart;g:=(x,y,z)->x+y+z;

NiM+SSJnRzYiZio2JUkieEdGJUkieUdGJUkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCg5JCIiIjklRjA5JkYwRiVGJUYl

phi:=(x,y,z)->x**2+y**2+z**2-1;

NiM+SSRwaGlHNiJmKjYlSSJ4R0YlSSJ5R0YlSSJ6R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsKiokOSQiIiMiIiIqJDklRjFGMiokOSZGMUYyISIiRjJGJUYlRiU=

F:=g(x,y,z)+lambda*phi(x,y,z);

NiM+SSJGRzYiLCpJInhHRiUiIiJJInlHRiVGKEkiekdGJUYoKiZJJ2xhbWJkYUdGJUYoLCoqJEYnIiIjRigqJEYpRi9GKCokRipGL0YoISIiRihGKEYo

Fx:=diff(F,x);

NiM+SSNGeEc2IiwmIiIiRicqJkknbGFtYmRhR0YlRidJInhHRiVGJyIiIw==

Fy:=diff(F,y);

NiM+SSNGeUc2IiwmIiIiRicqJkknbGFtYmRhR0YlRidJInlHRiVGJyIiIw==

Fz:=diff(F,z);

NiM+SSNGekc2IiwmIiIiRicqJkknbGFtYmRhR0YlRidJInpHRiVGJyIiIw==

Fphi:=diff(F,lambda);

NiM+SSVGcGhpRzYiLCoqJEkieEdGJSIiIyIiIiokSSJ5R0YlRilGKiokSSJ6R0YlRilGKiEiIkYq

fsolve({Fx=0,Fy=0,Fz=0,Fphi=0},{x,y,z,lambda});

NiM8Ji9JJ2xhbWJkYUc2IiQhK1FTRGcnKSEjNS9JInhHRiYkIisjcC1OeCZGKS9JInlHRiZGLC9JInpHRiZGLA==

evalf(%);

NiM8Ji9JJ2xhbWJkYUc2IiQhK1FTRGcnKSEjNS9JInhHRiYkIisjcC1OeCZGKS9JInlHRiZGLC9JInpHRiZGLA==

restart;f:=(x,y)->(r+x)*y;

NiM+SSJmRzYiZio2JEkieEdGJUkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsJkkickdGJSIiIjkkRjBGMDklRjBGJUYlRiU=

phi:=(x,y)->x**2+y**2-r**2;

NiM+SSRwaGlHNiJmKjYkSSJ4R0YlSSJ5R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsKCokOSQiIiMiIiIqJDklRjBGMSokSSJyR0YlRjAhIiJGJUYlRiU=

F:=f(x,y)+lambda*phi(x,y);

NiM+SSJGRzYiLCYqJiwmSSJyR0YlIiIiSSJ4R0YlRipGKkkieUdGJUYqRioqJkknbGFtYmRhR0YlRiosKCokRisiIiNGKiokRixGMUYqKiRGKUYxISIiRipGKg==

Fx:=diff(F,x);

NiM+SSNGeEc2IiwmSSJ5R0YlIiIiKiZJJ2xhbWJkYUdGJUYoSSJ4R0YlRigiIiM=

Fy:=diff(F,y);

NiM+SSNGeUc2IiwoSSJyR0YlIiIiSSJ4R0YlRigqJkknbGFtYmRhR0YlRihJInlHRiVGKCIiIw==

Fphi:=diff(F,lambda);

NiM+SSVGcGhpRzYiLCgqJEkieEdGJSIiIyIiIiokSSJ5R0YlRilGKiokSSJyR0YlRikhIiI=

solve({Fx=0,Fy=0,Fphi=0},{x,y,lambda});

NiQ8JS9JInhHNiIsJEkickdGJiEiIi9JJ2xhbWJkYUdGJiIiIS9JInlHRiZGLDwlL0YrLCQtSSdSb290T2ZHNiRJKnByb3RlY3RlZEdGNUkoX3N5c2xpYkdGJjYkLCYhIiQiIiIqJEkjX1pHRiYiIiNGOi9JJmxhYmVsR0Y0SSRfTDFHRiYjRjpGPS9GLiwkKiZGMkY6RihGOiNGKUY9L0YlLCRGKEZB

evalf(%);

NiQ8JS9JInhHNiIsJEkickdGJiQhIiIiIiEvSSdsYW1iZGFHRiYkRitGKy9JInlHRiZGLjwlL0YwLCRGKCQhK1NTRGcnKSEjNS9GJSwkRigkIisrKysrXUY2L0YtJCIrU1NEZycpRjY=

winkel:=evalf(arctan(1.5/(sqrt(3)/2))/Pi*180);

NiM+SSd3aW5rZWxHNiIkIispKioqKioqKmYhIik=

=> gleichseitiges Dreieck

restart;C:=7*10**(-6);

NiM+SSJDRzYiIyIiKCIoKysrIg==

deltaC:=0.3*10**(-6);

NiM+SSdkZWx0YUNHNiIkIisrKysrSSEjOw==

L:=0.22;

NiM+SSJMRzYiJCIjQSEiIw==

deltaL:=0.01;

NiM+SSdkZWx0YUxHNiIkIiIiISIj

T:=(L,C)->2*Pi*sqrt(L*C);

NiM+SSJURzYiZio2JEkiTEdGJUkiQ0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqJkkjUGlHSSpwcm90ZWN0ZWRHRjAiIiItSSVzcXJ0R0YlNiMqJjkkRjE5JUYxRjEiIiNGJUYlRiU=

TL:=D[1](T)(L,C);

NiM+SSNUTEc2IiwkSSNQaUdJKnByb3RlY3RlZEdGKCQiK1kyd1NjISM3

TC:=D[2](T)(L,C);

NiM+SSNUQ0c2IiwkSSNQaUdJKnByb3RlY3RlZEdGKCQiKz8wIkd4IiEiKA==

deltaT:=evalf(abs(TL*deltaL)+abs(TC*deltaC));

NiM+SSdkZWx0YVRHNiIkIiswPSRIVyQhIzg=

T:=evalf(T(L,C));

NiM+SSJURzYiJCIrOnpBKHooISM3

restart;f:=(x,y)->x**3-3*x**2+4*y**4-4;

NiM+SSJmRzYiZio2JEkieEdGJUkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCoqJDkkIiIkIiIiKiRGLyIiIyEiJCokOSUiIiVGNyEiJUYxRiVGJUYl

fx:=D[1](f);

NiM+SSNmeEc2ImYqNiRJInhHRiVJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmKiQ5JCIiIyIiJEYvISInRiVGJUYl

fy:=D[2](f);

NiM+SSNmeUc2ImYqNiRJInhHRiVJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwkKiQ5JSIiJCIjO0YlRiVGJQ==

y1:=(x)->-(fx(x,y)/fy(x,y));

NiM+SSN5MUc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwkKiYtSSNmeEdGJTYkOSRJInlHRiUiIiItSSNmeUdGJUYwISIiRjZGJUYlRiU=

zaehler:=denom(y1(x,y));

NiM+SSh6YWVobGVyRzYiLCQqJEkieUdGJSIiJCIjOw==

zaehler:=6*x-3*x**2;

NiM+SSh6YWVobGVyRzYiLCZJInhHRiUiIicqJEYnIiIjISIk

X:={solve(zaehler=0,x)};

NiM+SSJYRzYiPCQiIiEiIiM=

solve(f(0,y)=0,y);

NiYhIiIiIiJeI0YkXiNGIw==

solve(f(2,y)=0,y);

NiYqJCIiIyMiIiIiIiUqJl4jRiZGJkYkRiUsJEYjISIiKiZeI0YrRiZGJEYl