Which of the following is the correct condition for a function to be continuous at ?

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

Problem

Which of the following is the correct condition for a function

f

to be continuous at

x=a

? (a)

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

(b)

f(a)\text{ is defined and }\displaystyle\lim_{x\to a}f(x)\text{ exists}

(c)

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

(d)

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