-nx For n EN, consider the function f(x) = e on the interval [0, ∞). Let f(x) limn→∞ fn(x) for x = [0, ∞). (a) Describe the function f(x). Is continuous on [0, ∞). (b) Show that the sequence of functions (fn) does not converge uniformly on [0, ∞). (c) Does the sequence (fn) converge uniformly on the open interval (0, ∞)? (d) Show that for any a > 0, fn converges uniformly to f on the interval [a, ∞). =

Please

Sand is being dumped from a hopper railcar at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more sand is dumped). How fast is the base diameter increasing when the base is 18 feet long? Round your answer to three decimal places. ft/min

Let f(x) be differentiable for all x on R. Suppose that f(0) = -2  and that f'(x) ≤ 1 forall x on R. Use the Mean Value Theorem to show that f(4) ≤ 2.