Do You Really Know Your Limits?
Step-By-Step Video for Analyzing Limits using Movie Maker
Center #2
Developed by: Shavela Harvey
Washington-Marion Magnet High School
GLEs(Grades 11/12):
2. Evaluate and perform basic operations on expressions containing rational exponents
(N-2-H)
6. Analyze functions based on zeros, asymptotes, and local and global characteristics of the function (A-3-H)
7. Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and
constants in polynomial, rational, radical, exponential, and logarithmic functions (A-3-H)
24. Model a given set of real-life data with a non-linear function (P-1-H) (P-5-H)
Introduction:
You have been introduced to the topic of Limits in Calculus. We have focused on the graphical analysis of the limit of a
function and the algebraic computation of the limit of a function. In this learning center, you will compute the limits of
three rational functions algebraically and then you graph the three functions manually and investigate the limits of those
functions as the independent variable approaches specified values. Next, you will use Microsoft Mathematics and Math
Type in Microsoft Word to display and graph the three functions. Throughout this task, all of your procedures will be
recorded using the Flip Cam and compiled using Microsoft Movie Maker.
Essential Questions in the study of Limits:
1. How do you graph rational functions?
2. What is the meaning of a limit?
3. How do you calculate the limit of a rational function?
4. Are there any instances where the limit of a rational function may not exist? If so, examples.
5. How do you analyze limits on the graph of a function?
Task:
Initially, you wondered…”Why do I need to know this?” Well, I have just been notified by the Department of Homeland
Security and they have identified three mathematical models that represent the pressure of the deadly bombs that
terrorists have planted in the United States and these bombs are believed to be planted behind our school. They have
requested our help in calculating the limit of three functions that could assist them in deactivating the bomb. Oh yeah,
and one more thing, in preparation for any future attempts of attack, they have asked that we video our procedures.
Now, let’s make sure we calculate these limits correctly and quickly because obviously there are many lives at stake!
Process:
To accomplish this task, you and your team will complete the following step-by-step instructions:
a) In order to complete this task successfully, you and your team will select individual roles and responsibilities
b) Videographer: Your responsibility is to video the entire process from beginning to end using a FlipCam.
c) Worker: Your responsibility is to complete the manual recording of work on the worksheet. You will also be
responsible for narrating clearly the steps it takes to complete the worksheet assignment.
d) Verifier: Your responsibility will be to input and plot the functions from the worksheet into Microsoft Math to
verify the manual solutions. You will also be responsible for narrating clearly the steps it takes to verify the
computations and graphs in Microsoft Math. Use the Quicktip Sheet for Microsoft Math if necessary.
e) Movie Editor: You will be responsible for creating the Movie. You will edit to video in order to submit the final
project. To assist you with this task, please refer to the Quicktip Sheet for Windows Movie Maker Live if
necessary.
2) Before beginning this project, review the concept of a Limit via the following resource sites:
a) http://en.wikipedia.org/wiki/Limit_of_a_function
b) http://tutorial.math.lamar.edu/Classes/CalcI/limitsIntro.aspx
c) http://www.brightstorm.com/math/precalculus/polynomial-and-rational-functions/limits-of-rational-functions
(View the video clip on this link)
3) Your team will collaboratively complete the worksheet attached to this task by doing the following.
a) Calculate the limits for the three given rational functions.
b) Graph the three rational functions.
c) Identify the limit on the graph by the height of the function at each given point.
4) Your team will also verify the solutions and graphical analysis using Microsoft Math.
5) Your team will have to create a video using a Flipcam and a Movie Maker.
6) As a team, your team must review the final project for accuracy and effectiveness. Be sure to include a Title Page at
the beginning of the video and the Credits Page at the end so that all team members are acknowledged for their
work.
7) Save your final Movie project to the provided flash drive as: Team_(Group Number).
8) Email your final Movie project to the instructor at shavela.harvey@cpsb.org.
9) One member of your team will upload the final project to Mrs. Harvey’s Blackboard page. Select the Projects
navigation button on the left hand side and click on the link for Limits. Select Create Thread. In the subject area,
type: Team_(Group Number). Select Attach and then Submit.
Evaluation:
Please see the attached Task Checklist.
Reflective Question or Constructive Responses:
Upon completion of this learning center, ALL members of your team should be able to:
1) Compute the limit of a rational function.
2) Analyze the graph of a rational function in order to verify the limit at the identified value.
Complete a journal entry for the following question and post in our Discussion Board via the Limits link (be sure to
include all team members’ names in the subject line of your Discussion Board thread):
Evaluate and discuss the limits of the following functions:
1)
2)
Graph the following function and identify the limit as “x approaches 5” :
Place the response to your reflective question in Blackboard.
Adapted from resources found at the following website
http://webquest.sdsu.edu/templates/lesson-template1.htm
Based on a template from The WebQuest Page