Comments:

Overall very impressive, 22 assignments submitted with an average of 92. There
were several perfects and almost everybody got an A of some sort.

20 points for each part of each problem.

On 1c) some people used Taylor's thm which is okay, but it greatly
overcomplicated the matter. The problem can be done easily by applying part b.

On the second part of 2, some people showed the function was diff. at zero but
not that it was diff. within a neighborhood of zero. In R, this means showing f
is diff. on an open interval containing the origin. (The origin by itself not an
open set, as no ball centered at the origin is contained in the origin.)

I would also like to note that on 1b) some students went above and beyond to
show that fg is degenerate if (but not only if) f(0)=g(0)=0.

Additionally, on problem 2, some students (probably as a result of misreading
the problem), were able to complete the problem for f:Rn->R, interpreting x^2
as norm of x squared.

Just in case anybody cares.