We spent today talking more about limits. We showed how to make tables of function values as we approach a particular x-value of interest. We noted that for the polynomial, we could have just substituted the x-value of interest and gotten the right limit value. It turns out that this approach always works for limits involving polynomial functions.

We can often try the same technique on limits for rational functions, as long as we stay away from "bad" x's. If we approach an x-value that makes the denominator zero, our only hope is to factor the numerator and denominator of our rational function and hope for some cancellation. If we cannot both factor and cancel, the limit will either not exist or be infinite.

Thursday, we'll talk about the ways limits can screw up and the formal definition of limit. We'll also prove the existence of a couple of easy limits. See you then.