Day 9 (and 10): Limits Algebraically

There are too many ways to use algebra to solve a limit. This lesson is about factoring for rational expressions and rationalizing square root functions by multiplying top and bottom by a conjugate. However, I like to include synthetic division in the factoring since they'll need that skill later for integration. I also like to include problems where they need to get common denominators, FOIL, or use exponent rules. Based on their summer assignments, if I have a good crop of students, then this can be a one-day lesson. Otherwise, this is a two day lesson.

If I take two days to teach this lesson, I won't show them L'Hôpital on the first day thus making them factor their little hearts out for a whole class period. Then on the second day, that's when they can actually do this lesson.

What I don't do on this day is absolute value, piecewise functions, squeeze theorem, anything trigonometric, or anything of the indeterminate form ∞ - ∞.