Problem 3 (2 marks). Let f be a real-valued function defined on IR by f ( x) = x+x+1. (a) Show that for any sequence of real numbers { xko k=1 converging to 1, one has lim f (xk) = 3. (b) Does this suffice to establish that f is continuous at x = 1? (c) Argue whether or not f is continuous everywhere. (d) Expand your argument to show that any polynomial P: R - R of degree m defined by P ( x) = do + a j x + az x- + . .. + amxm is continuous