3. (10 Points) (True or False). You must justify your answer either mathematically or in well written English sentences, whichever is most appropriate. a. (1 Point) The lim f(x) depends on how f (a) is defined. x->a' b. (1 Point) If lim f(x) =0 and limg(x) =0, then lim / (x) must exist. x->a g(x) c. (1 Point) If f(x) = x -4 (x - 2) and g(x) =x+2, then we can say that f(x) and g(x) are identical functions. d. (1 Point) If lim f (x) =co and limg(x) =co , then lim [f(x)-g(x)]=0. e. (1 Point) If f(x) =x3, then f'(0) exists. f. (1 Point) The function f (x) = x has a derivative at x=0. g. (1 Point) d In()_ 1 dx h. (1 Point) For a constant, c, and a function, f(x), derivative of a constant times a function is def (x) _df (x) dx dx and the product rule gives def (x)_ cdf (x) + f (x) C. Hence, the two rules do not agree. dx dx i. (1 Point) If f"(a)=0, then f has an inflection point at a. j. (1 Point) If f (x) is continuous on a closed interval, then it is enough to look for at the points where f'(x) =0 in order to find its global (absolute) maxima and minima