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Given a function $f(x)$ whose domain is $\left[-4,6\right]$, is it possible to find $\lim_{x\rightarrow 6^+} f(x)?$

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The definition of $\lim_{x \to 6+} f(x)$ requires $f(x)$ to be defined for $x$ in some interval to the right of $6$. If that is not the case, then $\lim_{x \to 6+} f(x)$ does not exist.