Which of the following best describes a removable discontinuity of a function at ?

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

Problem

Which of the following best describes a removable discontinuity of a function

f

x=a

? (a) The one–sided limits

\displaystyle \lim_{x\to a^-}f(x)

and

\displaystyle \lim_{x\to a^+}f(x)

both exist but are not equal. (b)

f(x)

grows without bound as

x

approaches

a

from at least one side. (c)

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

exists and is finite, but either

f(a)

\text{is not defined} or

f(a)\neq \lim_{x\to a}f(x)

. (d)

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

, but

f'(a)

does not exist.