## University Calculus: Early Transcendentals (3rd Edition)

If we know $\lim_{x\to c}f(x)$ exists, we definitely can find its value by calculating $\lim_{x\to c^+}f(x)$.
If we know $\lim_{x\to c}f(x)$ exists, we definitely can find its value by calculating $\lim_{x\to c^+}f(x)$. That is because if $\lim_{x\to c}f(x)$ exists, then $\lim_{x\to c}f(x)=\lim_{x\to c^+}f(x)=\lim_{x\to c^-}f(x)=X$. $\lim_{x\to c}f(x)$ exists means that as $x$ approaches $c$, $f(x)$ approaches a single value. And either $x$ approaches $c$ from the left or the right, $f(x)$ would still approach that same value. Therefore, if we calculate $\lim_{x\to c^+}f(x)=X$, then we can conclude $\lim_{x\to c}f(x)=X$ as well.