Which of the following conditions guarantees that a real function is continuous at ?

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Which of the following conditions guarantees that a real function

f

is continuous at

x=c

? (a)

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

(b)

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

(c)

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

(d)

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