Limits of Functions Teacher Resources

For this calculus worksheet, students apply the properties of limits as they solve 40 functions with x approaching 1.

Push an engaging resource to the limit. The interactive allows learners to find a limit on quadratic functions graphically. Using sliders, pupils set the x-value for the limit and to move values from the left and right toward the limit.

Discover how to find limits using graphs. Viewers learn how to determine limits of a piecewise function at specific points by analyzing a graph. They consider both one-sided and two-sided limits.

Discover how to find limits of trigonometric functions. Viewers learn a strategy to calculate limits of trigonometric functions. They see how an expression can be rewritten to one whose limits are already known.

Rational functions become less mysterious when you know about limits. Individuals use an interactive to move a rational function on a coordinate plane and to investigate function values for certain x-values. They see how the limit...

Now do you see how limits relate to continuity? Viewers of this learn to find the value of a constant for a piecewise function that makes it continuous. They see how one-sided limits show that the derived constant is correct.

It's time to put it all together. Viewers of an informative video learn to connect multiple representations of limits. Given algebraic, tabular, and graphical representations of a linear piecewise function, they determine whether a limit...

Infinite limits just got infinitely more interesting. The 15th of 18 installments in Unit 1 - Limits and Continuity looks at infinite limits and vertical asymptotes of rational functions. Scholars review how to determine the locations of...

Learning about end behavior means it's close to the end of the unit. The 16th of 18 lessons in Unit 1 - Limits and Continuity has scholars watch a video to learn how limits at infinity can be used to determine horizontal asymptotes and...

Taking calculus doesn't mean one can forget all about algebra. Viewers of an educational video learn how to determine limits using algebraic properties. They apply basic operations to calculate limits and use substitution to find one-...

Do not cross the line while graphing. Provided with several coordinate axes along with asymptotes, pupils determine two functions that will fit the given restrictions. Scholars then determine other geometrical relationships of asymptotes...

Learn to find the slope through a single point. The interactive provides a visualization of how to find the slope of a tangent line. With the aid of the visualization, pupils see the definition of the derivative in action. Class members...

Take a free look. Released free-response questions from the 2003 AP® Calculus AB exam show how questions cover different topics. Pupils and teachers review the topics of bounded regions, particle movement, rates, relationships between...

It's called a removable discontinuity for a reason. After reviewing the conditions for a removable discontinuity to exist, scholars watch an informative video to learn how to remove the discontinuity. They look at several examples...

In this continuity and limits learning exercise, students solve and complete 4 different types of problems. First, they determine which of the limits shown exist and then, evaluate them. They also find which functions are continuous at a...

In this continuity worksheet, students solve 5 short answer problems about continuity.  Students determine where functions are continuous and find the limits of functions at points of discontinuity.

In this limits and functions worksheet, students solve 30 short answer questions about calculus  Students find limits, domain, range, tangent lines, derivatives, and composition functions.

In this math learning exercise, students examine the limits of the functions in two variables. Then the limits are measured for the functions to determine that they do not exist.

In this infinite limit worksheet, students compute horizontal and vertical asymptotes. They use trigonometric functions to find the limits of functions and compare results. This two-page worksheet contains examples and explanations and...

For this limits worksheet, students solve 6 short answer problems.  Students find the limits of functions, points of discontinuity, and the derivatives of functions.

Young scholars solve limit problems.   In this solving limit problems lesson plan, students use L'Hopital's Rule.  Young scholars apply L'Hopital's Rule to functions as long as the derivative of the top function and bottom function is...

In this function and limits worksheet, students identify a one-to-one correspondence and identify an inverse function. They compute limits of functions. This two-page worksheet contains five multi-step problems.

In this function worksheet, students determine the limits of functions, sketch graphs, and use the Intermediate-Value Theorem for functions. This two-page worksheet contains twenty-two problems.

In this limits activity, students find the limits of functions. They identify an equation of the line tangent to a curve. Students identify the velocity of objects. This two-page activity contains five problems.