Hints for realf-exercises.pdf:

1.  think about limits, from above and below
2.  no hint
3.  if it doesn't converge, it wanders back and forth
4.  look at g(x) = f^2(x)/2 + f'(x)
5.  define F(x) = int[a to x]f(t)dt, similarly G(x). You are comparing lengths of graphs of F and G
6.  Compare f$to a step function.
7.  Compare f(0) and f(1/3).
8.  Put several other functions in S first.
9.  If f and all derivatives are nonnegative, and f(0)=0, conclude f==0.