Lösungen

1

Remove["Global`*"]

Integrate[x y Sin[z]+y^2-x,{x,-1,0}]

Integrate[Integrate[x y Sin[z]+y^2-x,{x,-1,0}],{y,1,2}]

Integrate[Integrate[Integrate[x y Sin[z]+y^2-x,{x,-1,0}],{y,1,2}],{z,0,1}]

N[%]

2

Remove["Global`*"]

f[x_,y_]:=-x+x(y+1)^2;
f[x,y]

Integrate[f[x,y],x]+c1

Integrate[Integrate[f[x,y],x]+c1,y]+c2

Integrate[f[x,y],{x,0,Sqrt[1-y^2]}]

Integrate[Integrate[f[x,y],{x,0,Sqrt[1-y^2]}],{y,0,1}]

N[%]

3

Remove["Global`*"]

g1[x_,y_]:=Sin[x y]+Sin[x]-0.3;
g2[x_,y_]:=Sin[x y]+Sin[y]-0.3;

pl1=Plot3D[g1[x,y],{x,0,2},{y,0,2}];

pl2=Plot3D[g2[x,y],{x,0,2},{y,0,2}];

pl3=Plot3D[0,{x,0,2},{y,0,2}];

Show[pl1,pl2,pl3]

FindRoot[{g1[x,y]==0,g2[x,y]==0},{x,0},{y,0}]

FindRoot[{g1[x,y]==0,g2[x,y]==0},{x,1},{y,1}]

4

Remove["Global`*"]

p1={0,1.0};
p2={1,1.5};
p3={2,2.2};
p4={3,2.8};
p5={4,3.2};
points={p1,p2,p3,p4,p5}

plotpoints=ListPlot[points,PlotStyle->PointSize[0.02]];

linearfit=Fit[points,{1,x},x]

lplotline=Plot[%,{x,0,4}];

squarefit=Fit[points,{1,x,x^2},x]

splotline=Plot[%,{x,0,4}];

Show[plotpoints,lplotline];

Show[plotpoints,lplotline,splotline];