Exercise 1 - Chapter 2
(a)
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(b)
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(c)
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(d)
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(e)
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Maplets for Limits, Derivatives, and Tangent Lines
Calculus I Lab -- Fall 2002
prepared by
Douglas B. Meade
Department of Mathematics
University of South Carolina
Columbia, SC 29208
E-mail: meade@math.sc.edu
16 September 2002
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Purpose
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This week I had hoped to show you how to access some Maple-based graphical user interfaces (GUI) without the need to have Maple on your local computer. Unfortunately, I have encountered some technical difficulties that allow us to only make a half-step towards this goal.
Maple applets are called Maplets . MapleNet is a special web server that allows users to access a Maplet over the WWW. Maplets should work on any computer that has Maple installed.
I have prepared two simple Maplets for you to use to check your computation of limits and derivatives. To access these Maplets, you need to copy two files to your Z: drive on the CSM network. Download the files LimitCheck.maplet and DerivCheck.maplet from the course homepage. Once the files are downloaded, simply double-click on the file (using Windows Explorer) and the Maplet will open.
FunctionGrapher is one of the demonstration MapleNet Maplets. It is a nice tool that you can use to obtain the equation of the tangent line at a point, the graph of this line, and the derivative of the function. This Maplet can be accessed over the WWW at the URL: http://maplenet.math.sc.edu/maplenet/demo/FunctionGrapher.html.
Use the three tools mentioned above to evaluate the 10 problems listed below. Note that the majority of these 10 problems are taken from the Sample Test Problems at the end of Chapter 2 or 3. The other problems can be found in the text and are good practice for the exam. For your report, simply answer the question and indicate which Maple tool you used to check your result. But, be sure you can solve each problem by hand!
Before submitting your report check that you have answered each part of the two exercises.
The project is due in the dropbox at midnight, Thursday, September 19, 2002 . Do not put off work on this project until Thursday night!
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Exercise 1 - Chapter 2
(a)
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(b)
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(c)
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(d)
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(e)
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Exercise 2 - Chapter 3
(a)
Find g'(
) using a limit.
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(b)
/(x^2+1))](images/lab48.gif)
Use the Differentiation Rules to evaluate this derivative.
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(c)
Use the Differentiation Rules to evaluate the derivative of
, and f'(
).
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(d)
Find the equation of the tangent line to the graph of the above function at (1,
).
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(e)
Find all points on the graph of the above function where the tangent line has slope 1.
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