[1CZ]Suppose that a given function \(f : (a, b) β R\) is differentiable at every point of \((a, b)\) except \(x_ 0\), and that the limit \(\lim _{tβ x_ 0} f (t)\) exists and is finite. Show that f is also differentiable in \(x_ 0\) and that \(f (x_ 0 ) = \lim _{tβ x_ 0} f (t)\).
