Calculus
Lesson
04
Evaluating Limits
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The main method is simply Direct Substitution. As long as you are not
dividing by zero, putting a negative in a square root, or putting a non-positive
in a log, you should be fine.
1) Direct Substitution:
Example: 
2) Basic Properties for polynomials: Assume 
a) 
b) 
c) 
d) Same as c, except division, provided 
e) 
3) Basic properties of Radicals:
a) 
provided
that 
4) Composite Functions:
if 
then 
5) All trig functions: 
Techniques for finding limits
First try plugging in the number. If it works, then you're done.
If you try plugging it in and you end up dividing by zero, having a negative
argument of a square root, or a nonpositive argument of a logarithm, then your
are in trouble (probably no limit). However, if the form ends up being 0/0,
then maybe you can find the limit!
If 0/0 happens, factor and reduce. We can cancel the top and bottom since we never
actually let x=-1, so we never divide by zero.
If you can't factor because it has roots, then you must rationalize the part
with the roots, denominator or numerator.
multiply top and
bottom by conjugate.
Lastly, you must memorize:
You can then use these in other problems
