1) Consider the formula f(x)=lim(n-->infinity)((x^n)/(1+x^n)).

Let D={x:f(x) is an element of R}. Calculate f(x) for all x elements of D and determine where f: D-->R is continuous.

2) Let f: D-->R and suppose that f(x) greater than equal 0 for all x elements of D. Define sqrt(f)-->R by (sqrt(f))(x) = sqrt(f(x)). If f is continuous at c elements of D, prove that sqrt(f) is continuous at c.