Numerical Introduction to Limits

In this tutorial, we introduce an "intuitive" definition of a limit. After working through these materials, the student should be able to obtain numerical evidence for the calculation of limits; to determine what appears to be the limit from the numerical evidence; and to become aware of some of the problems in using numerical evidence for the calculation of limits.

Integration by Parts

We will use the Product Rule for derivatives to derive a powerful integration formula:

The Chain Rule

The Chain Rule allows us to use our knowledge of the derivatives of functions f(x) and g(x) to find the derivative of the composition f(g(x)):

Continuous Functions

In this tutorial, the definition of a function is continuous at some point is given. It is noted that this definition requires the checking of three conditions. Some examples applying this definition are given. Several theorems about continuous functions are given. Some examples of functions which are not continuous at some point are given the corresponding discontinuities are defined.

Antiderivatives / Indefinite Integrals

In this tutorial, we consider the problem where we are given the derivative F of some function f and we want to find the function f. We call f the antiderivative or indefinite integral of F. After looking at some examples, we discuss the relationship between two antiderivatives for the same function. We define the notion of initial conditions. Some basic properties of indefinite integrals are stated with examples provided. Applications of indefinite integrals are also provided.

Tangent Lines

In this tutorial, we define the tangent line at a point of the graph of a function. The tangent line is represented as the limit of secant lines. The approximation of the function by the tangent line is investigated graphically. After working through these materials, the student should be able to visualize the tangent line as the limit of secant lines; to visualize the tangent line as an approximation to the graph; and to approximate the slope of the tangent line both graphically and numerically.
 

Site Map  •  FAQs  •  Link to Us  •  Educational Gift Ideas  •  Add a Course  •  Contact Us

© 2008 Learning Link Finders, Inc. - All Rights Reserved - Modified on 01/01/08

All trademarks and registered trademarks appearing on the Docnmail.com website are the property of their respective owners.
By providing links to other sites, Learning Link Finders, Inc. does not guarantee, approve or endorse the information or products available
at these sites, nor does a link indicate any association with or endorsement by the linked site to Docnmail.com.