Today in class things got a little crazy. As we learned more about limits I was overwhelmed by a sense of scaredness and fright as I was not sure if I was for sure going to graduate. I am still not sure but with the help of Miss V all things remain possible. Anyways, let's get to it.
Limits of Polynomial and Rational Functions:
1. If p is a polynomial function and c is a real number, then lim x-->c p(x) = p(c).
2. If r is a rational function given by r(x) = p(x) / q(x), and c is a real number such that q(c) does not equal 0, then lim x--> c r(x) = r(c) = p(c) / q(c), q(c) does not equal 0.
Methods of Evaluating Limits:
1. Direct substitution (plug-in).
2. Cancellation technique (factor/cancel).
3. Rationalization technique (multiply radicals by conjugate).
Once you reach the intermediate form (0/0), use either the cancellation or rationalization method to evaluate the limit. If it contains a radical, use the rationalization technique. Finally, plug the value of x
in the equation using direct substitution. This will give you the value of the limit.
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