Limits — Introduction to limits

About this lesson

This unit introduces the concept of limits of functions. It begins by discussing unspecified quantities, such as 0/0, ∞ - ∞, and 0 × ∞, and clarifies that division by zero is undefined. The unit then defines the limit of a function at a point, explaining that it is the value a function approaches as x gets near a specific value from both the left and right sides. Students learn to find limits graphically from given figures and algebraically by completing tables of values. The text emphasizes that a function may have a limit at a point even if it is not defined there, and vice versa. Examples and exercises involve linear functions and rational functions like (x²-4)/(x-2). By the end, students should be able to evaluate limits using graphs and tables, and understand the distinction between a function's value at a point and its limit at that point.