Which one of the following statements is the necessary and sufficient condition for a…

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

Problem

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

f

to be continuous at

x=c

? (a)

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

(b)

f

is differentiable at

x=c

(c)

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

(d)

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