Create Your Formula Sheet In Advance

	There is online support for the Larson et al Calculus textbook.  They have free online support material for Chapters P, 1, 2, 3 at http://hmco.tdlc.com/public/calc7esample/
	Printable worksheets for graphical exercises can be found at mathgraphs.com.  Lots more can be found by going to www.tdlc.com.
	Hotmath  You can look at solutions to problems in exercise sets from a wide variety of mathematics textbooks including Calculus by Larson, Hostetler, Edwards, sixth , seventh, and eighth editions.  They have chapters 1 - 12 available.  Only a few solutions are still free (solutions to problems 15, 25, 35 in each section are free).
	For a nice set of review modules go to Visual Calculus: Limits and Continuity.
	Graphing calculators are great but can sometimes be misleading.  Here is an example from Visual Calculus that demonstrates some of the dangers in using a graphing calculator without any analytical knowledge from calculus to go along with it.
	Langara College has a nice set of notes with links to help on Limits and Continuity.
	Karl's Calculus Tutor also includes a lot of material on limits and continuity.
	UC Davis has a site with a lot of problems and worked out solutions dealing with limits, continuity, and other topics that we will cover later.
	You can compute limits using Derive or Maple on your computer to check your answers.
	You can also use the limit feature on the Vanderbilt Toolkit.  (Toolkit is currently unavailable.)
	Traces Animes  A really nice set of 2D and 3D WIMS graphing tools by XIAO Gang which will produce pictures and graphs that can then be saved and printed or used on a web site.  Traces Animes sample animation
	Here are some examples I will do the first day of class and here are some of the Chapter 1 examples I will do in later classes.
	Here is a Maple Worksheet demonstrating the Maple syntax for computing limits.
	Another nice set of tutorials with examples can be found at  SOS Mathematics.           SOS Math links to individual topics: Introduction to limits (and continuity) Properties of limits with examples Squeeze Theorem (Pinching or Sandwich Theorem) Limits and Infinity Continuity

Section 1.1:  This is a preview of calculus and you will not be tested on anything from this section until chapter two.  In chapter two you will need to be able to approximate the slope of a line tangent to the graph of a curve at a given point given only discrete data points along the curve.  For example, given the points (1.23, 6.41), (1.24, 6.48), (1.25, 6.55), (1.26, 6.64), (1.27, 6.75) on the graph of a function f, approximate the slope of the line tangent to the graph of  f  at (1.25, 6.55).  Here is an applet demonstrating the secant line approaching the tangent line and another java applet for the same thing.  Here is an applet demonstrating approximating the slope of a tangent line by using a secant "chord":  Group of Applets.  This links to a group of applets by MathinSite.  Click on Differentiation 1.

Section 1.2:  Here is a numerical introduction and a graphical introduction to limits.  You need to be able to find the limit of a linear function and verify your limit by satisfying the definition of limit.  (Epsilon-delta proof-Drill Problems)  Understand visually what the epsilon-delta definition of limit is telling you.  Here are some additional helpful pictures.  You need to be able to graphically find a delta to satisfy the definition of limit for a given particular value of epsilon and draw the related picture as shown in class (Visual Calculus example of this).  Here is another applet demonstrating the epsilon-delta definition of limit.  Click here to look at an animation relating to Example 8, page 54 in the text and visually demonstrating the Epsilon-Delta definition of limit.  Here is a Quicktime version of the example 8 animation and a Quicktime zoom version of the animation.

Section 1.3:  You will need to be able to use the limit theorems and the necessary algebra and trigonometry to analytically determine exact limits.  Note particularly the exercises in your text on pp68-9: 45-78.  Partial credit may be given for a numerical or graphical estimate of the limit.  Be able to apply the Squeeze Theorem.  The Harvey Mudd College limits tutorial may be helpful.  You need to be able to appropriately apply Theorem 1.2, p59, and you need to know when it does not apply.  Here is a link to the Visual Calculus drill problems on analytically determining limits.

Section 1.4:  You need to understand what it means for a function to be continuous.  (Applet demonstrating limit and continuity concepts)  You will need to be able to find the x-values (if any) at which a given function is not continuous and identify each discontinuity as removable or non-removable.  Note particularly the exercises in your text on pp79-80:  33-52, 57-60.  You will need to be able to compute one-sided limits (see exercises p79:  7-20).  Here is a java applet on one-sided limits.  The HMC continuity tutorials include an exploration and figures for types of discontinuities.  Click here to see an animation relating to P76, Example 7c.  Here is a link to the Visual Calculus drill problems on continuity for a piecewise defined function.

Section 1.5:  You will need to be able to identify limits that do not exist with the nature of their failure to exist being either positive or negative infinity.

You will need to be able to apply the Intermediate Value Theorem to verify that a continuous function has a zero between two given numbers.  Here is more on the IVT.  ExploreMath has a nice lesson on the Intermediate Value Theorem in its February, 2002 newsletter.

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        Lane Vosbury, Mathematics, Seminole State College   email:  vosburyl@seminolestate.edu

        This page was last updated on 08/21/14          Copyright 2002          webstats