What happens to a function $f(x)$ at $x=a$, if $\lim _{x \rightarrow a} f(x)=f(a)$ ?
If $f(x)$ is a function defined in its domain such that $\lim _{x \rightarrow \mathrm{a}} f(x)=f(a)$, then $f(x)$ becomes continuous at $x=a$.
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