Northeast Parallel Architectures Center, Syracuse University
Npac Reu Program: Infinite Limits for Rational Functions
This Northeast Parallel Architectures Center of Syracuse University site offers examples and instruction on infinite limits for rational functions.
Paul Dawkins
Paul's Online Notes: Calculus I: Limits
Learners explore limits. Topics investigated are continuity, limits at infinity, limit properties, tangent lines, and rates of change. Class notes, definitions, and examples with detailed solutions are included. The class notes are...
Northeast Parallel Architectures Center, Syracuse University
Npac Reu Program: One Sided Limits
Brief tutorial on special cases of the Cauchy Limit definition.
Texas Instruments
Texas Instruments: Piecewise Functions: Continuous Differentiable
This activity takes a discontinuous, piecewise defined function and redefines it to make it continuous and differentiable at the point of discontinuity.
Texas Instruments
Texas Instruments: Population and Limits
In this activity, students will consider a model of a population living in an unfavorable habitat. Given an initial population students will describe the population as timepases.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Formal Definition of a Limit
This Math Forum site is an inquiry by a student about the definition of a limit with a response by a professor. If you are confused by the student's inquiry don't worry, take a look at the doctor's response which explains what a limit is...
Texas Instruments
Texas Instruments: Limits Vertical and Horizontal Asymptotes
This activity explores graphically, numerically and symbolically the vertical and horizontal asymptotes of a rational function through the limit taking capability of the graphing calculator.
Texas Instruments
Texas Instruments: Taking It to the Limit
Students explore the concept of limits, both finite and infinite, using the graphing calculator. Each rule has a set of examples and a section for the students to try other examples to create a basis of understanding of each of the rules.
Paul Dawkins
Paul's Online Notes: Tangent Lines and Rates of Change: Practice Problems
This section introduces two problems: rate of change of a function and tangent lines to functions. Both of these problems will be used to introduce the concept of limits.
Massachusetts Institute of Technology
Mit: Open Course Ware: Differentiability and Continuity
The activity investigates differentiability and continuity. The resource consists of online textbook chapters and exam questions with solutions on non-differentiable behavior. All documents were created from scanned original files and...
CK-12 Foundation
Ck 12: Analysis: Real Zeros of Polynomials
[Free Registration/Login may be required to access all resource tools.] In this lesson students solve problems involving polynomial and rational functions. Students examine guided notes, review guided practice, watch instructional videos...
CK-12 Foundation
Ck 12: Analysis: One to One Functions and Their Inverses
[Free Registration/Login may be required to access all resource tools.] Definition and exploration of 1 to 1 functions and their inverses
Paul Dawkins
Paul's Online Notes: Continuity: Practice Problems
Practice exercise reviews the concept of continuity and how it relates to limits. Also, provides practice with the use of the Intermediate Value Theorem.
CK-12 Foundation
Ck 12: Analysis: Limits and Asymptotes
[Free Registration/Login may be required to access all resource tools.] Introduction to end behaviors, limits, asymptotes and limit notation.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Derivadas. Aplicaciones. Optimizacion.
In Spanish. This interactive unit is intended to show you how to calculate the derivative of a function and the application of the derivative in other sciences.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Asintotas
In this unit you will learn to calculate the limits of a function and the equations of the vertical, horizontal and oblique asymptotes from its graph.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Continuidad De Funciones
In Spanish. In this interactive unit you will be able to tell if a function is continuous from its graph, understand the concept of continuity of functions and to distinguish between the different types of discontinuities either...
Other
Seton Hall University: Limits
Detailed tutorial which defines, explains, and has examples of various function limits.
Wolfram Research
Wolfram Math World: Leibniz Integral Rule
This page discusses the Leibniz Integral Rule, which concerns "the differentiation of a definite integral whose limits are functions of the differential variable."
Wyzant
Wyzant: Function Graphing Calculator
Students input a function in either y= of f(x)= form, and then the site from WyzAnt does the rest! A detailed graph is shown in less than a second. Students can change the window used to view the graph as well as whether to have...
Math Graphs
Houghton Mifflin: Math Graphs: Derivative and Limits [Pdf]
Students sketch the graph of the derivative and examine the limits of a given function. The example is available in PDF format.
Paul Dawkins
Paul's Online Notes: Limit Properties: Practice Page
Provides nine practice problems that review the properties of limits used in computing limits.
Paul Dawkins
Paul's Online Notes: The Definition of the Limit: Practice Problems
Practice exercise provides problems that review limits including how to use the definition to compute a limit.
Windstream
Ojk's Precalculus Study Page: The Number E and the Function E^x
An introduction to the natural exponential function, beginning with the limit definition of the irrational number e. Includes several examples and exercises with solutions which deal with the compound interest formula.