Let fn RR be a sequence of continuous functions which converg uniformly to a function f : R → R. Let (xn) be a sequence of re numbers which converges to x E R. Show that fn(n) → ƒ(x).

Say f(x) is positive and strictly increasing on the interval [a, b]. Show that the lower sum calculated with n rectangles is less than the upper sum calculated with n rectangles.

Let f and g be continuous functions from R to R. Show that the function F(x) = min{f(x), g(x)}  is a continuous function.