Which of the following statements is always true regarding the existence of the…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which of the following statements is always true regarding the existence of the two-sided limit

\displaystyle\lim_{x\to a}f(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