August 20 - Limits continued

We started class today with a quiz on solving trig equations.

I covered a number of topics related to limits today and I'm hoping that most if not all of this was review. We worked some examples about limit properties (basically limits behave in a pleasing, intuitive way) and then talked about algebraic techniques for evaluating limits.

As a general rule, the first step in evaluating a limit is to do direct substitution. If this yields a value, then often that is the limit (nice functions). More often however, direct substitution gives a result of 0/0 which is an example of an indeterminate expression. For the student, this implies there is more work to do in order to evaluate the limit or to conclude that the limit doesn't exist.

We worked two examples - one showing the factor/cancel algebra and the other showing the multiplying by the conjugate algebra.

Finally, I reminded students that there are two trig limits with which they should be familiar. They are:

lim ((sin x) / x) = 1
x->0

and

lim (1 - cos x) / x = 0
x->0

We will talk about proofs of these on Monday.

There will be a limits quiz on Monday.