Limits and Continuity — Limit of a function at infinity

About this lesson

This unit focuses on the concept of limits of functions at infinity. It begins with an activity using graphs and tables to observe how function values approach a certain number as x increases indefinitely. The unit then introduces the formal definition and rules for finding limits at infinity, including the basic rule that the limit of 1/x^n as x approaches infinity is 0 for positive integer n, and that the limit of a constant is the constant itself. It also states that the algebraic rules for limits at a point extend to limits at infinity. The unit provides worked examples and exercises for evaluating limits of polynomial and rational functions at infinity, including cases where the degrees of numerator and denominator are compared. It also covers limits involving radicals and expressions with square roots, often using algebraic manipulation such as dividing by the highest power of x or rationalizing. By the end of the unit, students should be able to compute limits at infinity algebraically and graphically, and apply these skills to real-life problems such as determining the cost per card as production becomes very large.