Which of the following conditions is sufficient to conclude that has a removable…

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

Problem

Which of the following conditions is sufficient to conclude that

f

has a removable discontinuity at

x=c

? (a) The left-hand and right-hand limits at

x=c

both exist but are not equal, regardless of

f(c)

. (b)

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

does not exist, but

f(c)

is defined and finite. (c)

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

exists and is finite, but

f(c)

is either undefined or not equal to that limit. (d)

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

, yet

f'(c)

does not exist.