Limits and Continuity — Finding the limit of a function algebraically

About this lesson

This unit teaches students how to find the limit of a function algebraically, building on earlier graphical and numerical methods. It introduces theorems for limits of polynomial functions and general limit laws (constant multiple, sum, product, quotient, power). It covers direct substitution, and when that leads to an indeterminate form like 0/0, it shows techniques: factorization, long division, synthetic division, and using conjugates. The unit also presents a theorem for limits of the form (x^n - a^n)/(x - a) and its corollaries, with examples and exercises. Applications include finding limits of rational, radical, and trigonometric functions, and a word problem about profit and a cardboard box volume activity. By the end, students should be able to compute limits algebraically for various function types, handle indeterminate forms, and apply limit theorems.