Ways to solve these types of indeterminations? I'm looking for this type of indeterminations and what I have to do to solve these:
$\lim\limits_{x\to\infty}{f(x)=\dfrac{\infty}{\infty}}$
$\lim\limits_{x\to\infty}{f(x)=\infty-\infty}$
$\lim\limits_{x\to\infty}{f(x)=\dfrac{0}{0}}$
$\lim\limits_{x\to\infty}{f(x)=\dfrac{n}{0}},n\not=0$

EDIT:
Could anyone post any examples of these indeterminations?

The answer will generally depend on the particular $f(x)$ (though for cases 1 and 3 there is a general tool, L'Hopital's Rule if you already know it, that will often work, and for case 4 you can always say the limit does not exist).
The first limit type may be done by L'Hopital's rule (if both numerator and denominator are differentiable), or by algebraic manipulations dependent on the particular $f(x)$.
The second type of limit will require some algebraic manipulations (usually particular to the $f(x)$ in question) to bring it to some manageable form.
The third type may be done by L'Hopital's rule if both numerator and denominator are given by differentiable functions; or again by algebraic manipulations that depend on the particular form of $f$.
In the fourth case, the limit does not exist. If $n\gt 0$ and the denominator is always positive for large enough $x$, then the limit will be $\infty$; same if $n\lt 0$ and the denominator is negative for all large enough $x$. If $n\gt 0$ and the denominator is negative for all large enough $x$, or $n\lt 0$ and the denominator is always positive for large enough $x$, then the limit will be $-\infty$. Otherwise, the limit will simply not exist and not diverge to either $\infty$ or $-\infty$.
