Which of the following is the necessary and sufficient condition for a function to be…

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

Problem

Which of the following is the necessary and sufficient condition for a function

f

to be continuous at

x=a

? (a)

f

is differentiable at

x=a

(b)

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

(c)

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

(d)

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

exists and

f(a)

is defined