From the exam problem collection, do:

8

73 

88

123

125

Consider problem 132 (given for seminar 08): We found that (1,0) is a local minimum except for a=0. Put u(a)=f(1,0), and find u'(a). 

The following was stated in a seminar, but do it yourselves:
Let A be a square matrix, and I the identity of the same order, and suppose that the kth power A^k tends to 0 as k -> infinity.
Show that (I-A) has an inverse, and that this is equal to I + A + A^2 + A^3 + ...