University Calculus: Early Transcendentals (3rd Edition)

Can not conclude anything about $\lim\limits_{x \to 1}f(x)$ until we know the values of function f(x) near x = 1.
The existence and non-existence of the limit as x approaches to c does not depend on whether the function is defined or not defined at x=c. So, if $f(1) = 5$, it is not necessary that the limit should exist as x approaches 1.