Define infinite limits like [math]\lim_{x\to a} f(x) = \infty[/math] and [math]\lim_{x\to a} f(x) =- \infty[/math].
Define limits at infinity like [math]\lim_{x\to\infty}f(x)=L[/math] and [math]\lim_{x\to-\infty}f(x)=L[/math].
Define infinite limits at infinity like [math]\lim_{x\to\infty}f(x)=\infty[/math] and [math]\lim_{x\to-\infty}f(x)=\infty[/math] and so on.