Limits and Continuity — Existence of the limit of a function at a point

About this lesson

This unit covers limits of trigonometric functions and the existence of a limit of a function at a point. It begins with a series of exercises on finding limits of expressions involving sine, cosine, tangent, and their combinations as x approaches 0 or other values. The second part introduces the concepts of right-hand limit, left-hand limit, and the condition for a limit to exist (both one-sided limits must be equal). It uses piecewise-defined functions and graphs to illustrate when a limit exists or does not exist. Students are expected to compute limits of trigonometric expressions and to discuss the existence of limits for piecewise functions, including cases where the function is not defined on one side of the point.