Let aER. Let f and g be functions defined at least on an interval centered at aER, except possibly at a. Is each of the following claims true or false? If it is false, show it with a counterexample. If it is true, prove it. (The proof should be a short, "one-line" proof using the properties of limits you already know. Do not use the formal definition of limit. No epsilons allowed in this question.)

Let a E R. Let f and g be functions defined at least on an interval centered at a E R, except possibly at a. Is each of the following claims true or false? If it is false, show it with a counterexample. If it is true, prove it. (The proof should be a short, "one-line" proof using the properties of limits you already know. Do not use the formal definition of limit. No epsilons allowed in this question.)| (i) If lim [f (x) - g(x)] exists and lim f(x) exists, then lim es() exists. Please fill the blank with x-> a x- a TRUE or FALSE. Final Answer This claim is