## Thomas' Calculus 13th Edition

The limit values can not be determined $\lim\limits_{x \to 1}f(x)$ until we have the values of function $f(x)$ near x = 1.
The existence and non-existence of the limit $\lim\limits_{x \to 1}f(x)$ does not depend on whether the function is defined or not defined at the point near $x=c$. Thus, when $f(1) = 5$, then it is not necessary that the limit would exist as $x \to 1$.