Limits — Finding the limit of a function algebraically

About this lesson

This unit teaches students how to find the limit of a function algebraically, without relying on tables or graphs. It covers limits of polynomial functions through direct substitution, and introduces theories for combining limits (such as sums, products, quotients, and powers). The unit also explains how to handle cases where direct substitution gives an undefined expression, using techniques like factorization and using conjugates to simplify the function before taking the limit. Examples include limits involving rational functions, square roots, and expressions that simplify to a constant. By the end, students should be able to compute limits of polynomial functions, apply limit laws, and use algebraic manipulation (factorization, conjugation) to evaluate limits that initially appear indeterminate.