(∫_(-π/2)^(π/2))Cos[x]\[DifferentialD]x

A={{1,-5},{-3,-1}};
xold={1,1};
For[k=1,k≤2,k++,
ynew=A.xold;
xnew=ynew/Norm[ynew];
lambda=xold.ynew;
xold=xnew;
]
N[xnew]
N[lambda]
Eigensystem[N[A]]//MatrixForm

Print["uppgift 6"];
f[x_]=(E^(-x))+2x;
g[x_]=x-((f'[x])/(f''[x]));
Print["Svar:",FindMinimum[f[x],x]]

f'[0]

Minimize[{x1^2+2*x2^2+x2,x1==2*x2},{x1,x2}]

DSolve[{y'[t]==t+2y[t],y[0]==1},{y[t]}]

DSolve[{y'[t]==t+2 y[t],y[0]==1},y[t],t]

(1/9)*(4/9)