$f(0) = 1\,\,,\,\,\mathop {\lim }\limits_{x \to {0^ + }} f(x) = a\,\,,\,\,\mathop {\lim }\limits_{x \to {0^ - }} f(x) = - a$
$a = 0 \Rightarrow f(0) \ne \mathop {\lim }\limits_{x \to 0} f(x)$
$a \ne 0 \Rightarrow \mathop {\lim }\limits_{x \to {0^ + }} f(x) \ne \mathop {\lim }\limits_{x \to {0^ - }} f(x)$
تابع در $x = 0$ پیوسته نیست.