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.

Limit the view of sequences on both sides of the axis. Learners explore an alternating sign sequence. Using a graphical display of the first 10 terms of the sequence, pupils determine the formula for the general term. they then use the...

What does it mean if young mathematicians cannot put the squeeze on a sequence? Learners investigate a divergent sequence and find the formula for the nth term. Using the definition of a limit of a sequence, pupils try to find the limit...

Take a look at another alternating sequence. The resource provides a graphical display of a sequence that alternates between two values. Pupils use the display to determine whether the sequence has a limit. Given a theory of limit,...

Limits can provide some valuable information about graphs. A slider interactive lets learners see the behavior of a graph around asymptotes. They investigate relationships between limits and asymptotes.

Chase a periodic moving limit. Learners graphically determine the limit of the tangent function at different input values. Using sliders, pupils find out whether the tangent function approaches the same value from the left and the right....

A one-sided limit is no less important than a two-sided limit. Young mathematicians use an interactive to match limit notation to graphs. The exercise requires interpreting how one-sided limits connect to features of graphs.

Put a squeeze on a sequence. An interactive provides a graphical display of a sequence. Using the graph, learners determine the algebraic expression for the sequence. Pupils use the general definition of a limit of a sequence to find the...

Limits are made easy through graphs and tables. An easy-to-use interactive lets users change a function on a coordinate plane. They relate graphs and tables to the limit at a specific value.

Not everything that's one-sided is bad. A slider interactive aids learners in investigating one-sided limits from graphs. A set of challenge questions assesses their understanding of the relationship between one- and two-sided limits.

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...

Discontinuities in the graph? No worries. Pupils investigate the limit of a function given graphically using an interactive. The graph has removable and jump discontinuities.

There are an infinite number of reasons to use the resource. Scholars drag vertical and horizontal lines to the graph of a rational function to identify all asymptotes. They investigate the connection between asymptotes and limits to...

Limits to infinity are simple to find if you can compare numerators and denominators. Users of the interactive drag expressions to match with their limit as x approaches infinity. A set of challenge questions assesses their groupings.

There's no limit to how useful the resource can be. Scholars use a slider interactive to investigate limits from graphs. They take both one-sided and two-sided limits into consideration.

If any of the limiting factors in an environment change, both animal and plant populations also change. The video explains two different models of growth and the impact of limiting factors. It highlights the carrying capacity of an...

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...

Geometric series either get bigger or approach a single number. So, how do you know which it is? An interactive presents three different geometric series with varying common ratios. With the aid of patterns, pupils determine values of r...

The more rectangles, the better the estimate. Using the interactive, pupils explore estimating the area under a curve using left-hand sums. Learners respond to challenge questions on how to get better estimates using the same technique.

How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...

Why do planets orbit the sun in ellipses when moons orbit their planet in circles? Pupils control the semi-major axis, eccentricity of the orbit, and position angle. The resulting orbital appears with the related force vectors as...

Determine how many three-player teams you can make from five players. Pupils drag dots representing players to create a list of teams they can form with a limited number of players. They then find out the number of teams one...

Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...

Does the accuracy of the first guess make a difference down the line? Learners investigate the effects of the iterative process of finding roots, using Newton's Method. By moving the initial guess of a root on a graph, pupils observe the...