TITLE: List of techniques to evaluate limits?
QUESTION [12 upvotes]: I'd like to make a complete list of techniques to evaluate a limit.

Definition of the limit
Continuous functions
Algebra of limits
Addition, multiplication, division
Composition
Inverse function
Showing inequalities
Squeeze theorem
Rewriting, try to factor out common factors in numerator and
denominator
Rationalizing the denominator
Substitutions, in particular the $1/t$ substitution. 
Use of derivatives, l'Hôpital's rule and Taylor series.
If $\lim_{x\to a} f(x)=1$ and $\lim_{x\to a} g(x)=\infty$ then $$\lim_{x\to a} f(x)^{g(x)} = e^{\lim_{x\to a} g(x)[f(x)-1]}$$
for $$0^0\quad and\quad \infty^0 \quad form \implies $$
$$\lim_{x\to a} f(x)^{g(x)}=e^{\lim_{x\to a}[g(x) \log_e{f(x)}]}$$

However the list seems so short. Are there any other good strategies or techniques to solve limits?

REPLY [3 votes]: The list of techniques to evaluate a limit that you have given above covers most of the non-elementary limit problems. Below I have given a few results that will be helpful in evaluating certain limit problems$:$
$ \bullet \ $ Assume that $f:(-a,a) \setminus \{0\} \rightarrow \Re \ $. Then $\lim_{x\to0}f(x)=l \ $ if and only if $ \ \lim_{x\to0}f(\sin(x))=l. $
$\bullet \ $ Assume that $f:(-a,a) \setminus \{0\} \rightarrow \Re \ $ . If $ \lim_{x\to0}f(x)=l \ $ then $ \lim_{x\to0}f(\left \vert {x} \vert \right) = l. $
$\bullet \ $ $ lim_{x\to \infty} \left(1+\frac{1}{x}\right)^x = e$ 
$\bullet$ $ lim_{x\to 0} (1+x)^\frac{1}{x} = e $