Which of the following conditions is REQUIRED for the limit to exist?

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

Problem

Which of the following conditions is REQUIRED for the limit

\displaystyle \lim_{x\to c} f(x)

to exist? (a)

f(c)

equals the common value approached by

f(x)

x\to c

. (b)

f

is defined at

x=c

. (c) The left-hand and right-hand limits at

c

are equal and finite. (d) Both one-sided limits at

c

are finite, even if they are unequal.