Math 131
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School
Valparaiso University *
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Course
131
Subject
Mathematics
Date
Feb 20, 2024
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docx
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Math 131, Lab 1: Introduction Lab
Name(s): Michael Swan
Honor Code: I have neither given nor received, nor have I tolerated others’ use of unauthorized aid.
·
Suggested Technology:
Microsoft Office (Word, Excel), Wolfram Alpha, Desmos
·
Goals:
By the end of this lab, you should be able to…
o
Input functions using a spreadsheet and Wolfram Alpha
o
Graph functions using Wolfram Alpha over defined bounds
o
Solve equations using technology
In the Lab
In this lab we will explore the use of technology to improve conceptual understanding of the material in Calculus I. Save
this Word document with your last name in the file name. As you work through the lab, record your work in this document. Submit your final draft of this lab by uploading your completed Word file on Blackboard. This lab can be completed on any computer
regardless of software. You may wish to reference this lab for future topics. 1.
We may all be used to evaluating a function on paper and by hand, however using different computational software requires that we declare which function we wish to manipulate and study.
a.
Input the function into Wolfram Alpha (
www.wolframalpha.com
) using the Math
Input
Commands. Select “=” on the right side of the input bar when you are finished. Now, input the same function into Desmos (
www.desmos.com
). When entering exponents into Desmos, you can use the “^” character. Make sure to use parentheses where needed. What is the difference in the output of the two software programs? What sort of information is displayed?
Wolfram shows more than just graphs. Wolfram shows the alternate forms, expanded form, etc. Desmos just shows the graph as if you used a graphing calculator.
b.
You can evaluate the function in Wolfram Alpha at a given point by adding the following command format: “evaluate at x = x
0
”. Use this format to evaluate the function at x = 2, x = -1, and x = 135. Is there a difference if you use “at x = 2.0”?
X=2 --> 4/5 x=-1 --> ½ x=135 --> 2,460,105/18,226
The only difference is that the answer is in decimal form instead of a fraction.
c.
You can evaluate the function in Desmos at a given point by using function notation. For example, in the first line and in the second line. Use Desmos to evaluate the value of the function at x = 1.7, and x =.
X=1.7 --> 0.3889 x=root 2 --> 1.4803x10^-16
d.
Now use a spreadsheet (Google Docs, or Microsoft Excel) to evaluate the function. Enter the function as a formula by selecting a cell and entering an equal
sign first. Not enter the expression for the function. Instead of entering x, select a different cell in the sheet that represents the value of x. Use parentheses to separate the numerator from the denominator. Now evaluate the function at x = 20, x = –5, and x = 101 by changing the values of x in the selected cell. X=20 --> 19.850
X=-5 --> -4.423
X=101 --> 100.970
2.
Now consider the graph of the function. a.
Using Wolfram Alpha or Desmos, snip an image of the graph of the function. Your image needs to include ONLY the parts of the graph that are important. Please do not submit a screenshot of the whole computer screen. Insert the image below.
b.
You can also change the endpoints of the graph in Wolfram Alpha by using the following format: “plot from x = x
1
to x = x
2
”. Plot the function in Wolfram Alpha from -3 to 3 and insert the output below.
c.
You can graph a similar image in Desmos using the following format: . Practice using this command format in Desmos.
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d.
You can use the ‘solve’ command in Wolfram Alpha to solve an equation: Enter “solve.” Use this command to solve for the roots of f(x)
.
X=0
X=± sqrt (2)
3.
You can use the plot command in Wolfram Alpha to plot multiple functions at the same time as well. This is done by using the command format: “plot,
sin(x).”
It is much easier to plot multiple functions in Desmos by just typing the functions into separate lines.
a.
Plot the functions and from x = –5 to x = 2. Insert the output below.
X=-5 --> x= 0, x=
± sqrt (2)
X=2 --> x= 0, x=
± sqrt (2)
b.
Use the solve command in Wolfram Alpha to find the point(s) of intersection between f(x)
and g(x)
. Use Desmos to check these intersection points in decimal form. -1.414 and 1.414
4.
These are only some of the things that Wolfram Alpha can do. Your final challenge is finding one or two features of Wolfram Alpha that were not introduced before. Explain what this feature is and does.
It can solve matrices. This means it can bracket 4 or 6 numbers together and find the completed matrix you were meant to find.
5.
These are only some of the things that Desmos can do. Your final challenge is finding one or two features of Desmos that were not introduced before. Explain what this feature is and does.
Desmos can find medians, modes, minimums, and maximums. This helps in case we need to solve for patterns in graphs.