Evaluating Limits of Function Products and Quotients Graphically

Khan Academy

This video provides a clear, step-by-step tutorial on evaluating limits for combined functions using graphical data. The narrator guides viewers through two distinct examples: the limit of a product of functions and the limit of a quotient of functions. By applying fundamental limit properties, the video demonstrates how to break down complex expressions into simpler components that can be evaluated visually from provided graphs. The content explores key calculus themes including the product and quotient laws for limits, the distinction between a function's value and its limit, one-sided limits (left-hand vs. right-hand), and continuity. It specifically addresses the scenario where a limit does not exist due to division by zero, helping students recognize this critical mathematical condition. For educators, this video serves as an excellent bridge between algebraic limit laws and graphical interpretation. It is particularly useful for helping students develop visual intuition for calculus concepts. Teachers can use this resource to reinforce how to read function behavior near specific points and to spark discussions about why limits might exist even when a function is undefined at a point, or conversely, why they might fail to exist.