Curated OER
Is There a Limit to Which Side You Can Take?
Calculus young scholars find the limit of piecewise functions at a value. They find the limit of piecewise functions as x approaches a given value. They find the limit of linear, quadratic, exponential, and trigonometric piecewise...
National Security Agency
Multiple Representations of Limits
After an introductory activity to demonstrate the theory of a limit, additional activities approach a limit from graphical, numerical, and algebraic methods. The activity looks at the multiple ways of understanding and evaluating a limit.
Curated OER
Worksheet 5: Property Limits and the Squeeze Theorem
In this math worksheet, students answer 6 questions regarding given limits in a table of data, properties of limits and the Squeeze Theorem.
Curated OER
Explorations 5: Introduction to Limits
In this limit learning exercise, students find the interval values of given functions. They identify constants, and plot graphs. This three-page learning exercise contains approximately 20 problems.
Curated OER
Worksheet 10 - Limits
In this limits worksheets, students graph tangent lines and determine the slope of a secant line. This one-page worksheet contains six multi-step problems.
CK-12 Foundation
Limits of Polynomial and Rational Functions: Evaluating the Limits of the Quadratic Function
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.
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 3)
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...
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 2)
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...
CK-12 Foundation
Infinite Limit Type: Properties of Limits
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.
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 4)
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,...
Curated OER
Open Sets, Limits, Continuity
In this open sets worksheet, students give characteristics of an open set under given conditions. They graph functions and define limits. This two-page worksheet contains 3 multi-step problems with explanations.
CK-12 Foundation
Basic Trigonometric Limits: Evaluating Limits of tan(x)
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....
Curated OER
Worksheet 4: Limits
In this limits worksheet, students evaluate limits and graph given expressions. They classify graphs as removable discontinuities, jump discontinuities, or asymptotes. this two-page worksheet contains seven multi-step problems.
Curated OER
Introduction to Limits
High schoolers practice using graphing calculators and spreadsheets as they explore numeric limits using sequences and functions. They complete a sequencing worksheet, and determine which sequence corresponds to story a story called...
Curated OER
Worksheet 35 - Limits
In this limit worksheet, students compute the limits of given equations. They rewrite limits in indeterminant form. This one-page worksheet contains approximately 18 equations.
Curated OER
Worksheet - Limits
For this limit worksheet, students give examples of described sequences and find the limits. They compute numbers in the Fibonacci sequence. This one-page worksheet contains six multi-step problems.
Curated OER
Finding the Limit: Piecewise Functions and Graphs
This pre-calculus worksheet is short, yet challenging. High schoolers calculate the limit of piecewise functions, rational functions, and graphs as x approaches a number from the positive or negative side. There are four questions.
CK-12 Foundation
One-Sided Limit Type: Limit Notation and Graphs
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.
Curated OER
Worksheet 4: Graphs and One-Sided Limits
In this math worksheet, students answer 6 questions regarding functions, graphs, one-sided limits, intercepts, vehicle speed and wheel rotation.
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 1)
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...
CK-12 Foundation
Evaluate Limits Using Graphs and Tables: Where Is That Limit?
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.
CK-12 Foundation
One-Sided Limit Type: One-Sided Limits
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.
CK-12 Foundation
Infinite Limit Type: Evaluating Limits of Rational Functions
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...
CK-12 Foundation
Evaluate Limits Using Graphs and Tables: Evaluate the Limits
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.
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