1. Study the stability of the limit cycle r=1 for the system given in polar coordinates by the equations r ? =(r^2 -1)(2x-1) , φ ? =1 . (where x=rcosφ ).
2. Solve the equation dy/dx =y+h N , where h N (x)=N for |x-1|<1/2N and 0 for |x-1|≥1/2N with initial condition y(0)=0 , and find the limit of the solution as N→∞ .
3. Prove that δ(αx)=δ(x)/|α| . ( In particular, if α=-1 , we can see δ(x) is an even "function".