Which of the following statements is always true regarding the existence of the two-sided limit x→alimf(x)?
a) It exists if and only if f(a) is defined.
b) It exists if and only if f is bounded on an open interval containing a.
c) It exists if and only if the left-hand and right-hand limits at x=a both exist and are equal.
d) It exists if and only if f is continuous at x=a.