Wolfram mathematica software project calculus i (mat

wolfram mathematica software project

Calculus I (MAT 221)

Mathematica Project 2

For this project, we will be looking at implicitly defined curves. The goal is to be able to plot an implicit curve using Mathematica, find the derivative of that implicit curve, and then plot tangent lines together with the original curve. We will be using the operation ContourPlot to graph these implicit functions. For example, to plot the unit circle x^2+y^2 = 1 on a window of −1.5 ≤ x ≤ 1.5 and −1.5 ≤ y ≤ 1.5, we would write the code as:

ContourPlot[x^2 + y^2 == 1 , {x,−1.5,1.5} , {y,−1.5,1.5}]

1) Let’s start by looking at the the basic hyperbola, x^2−y^2 = 1.

a) Plot this hyperbola.

b) In Mathematica write a detailed step by step process on how to find the derivative, dy/dx, by using implicit differentiation.

c) Using the Derivative operation in Matheamtica, confirm your derivative from the previous step.

d) Using this, find the derivative at the point (−2,√3). (-2, radical (3))

e) Graph the tangent line on the same plot as the hyperbola.

2) A famous implicitly defined curve is the Lemniscate of Bernoulli. This curve is defined by: (x^2 + y^2)^2 = 4(x^2 −y^2).

a) Plot the Lemniscate of Bernoulli.

b) In Mathematica write a detailed step by step process on how to find the derivative, dy/dx, by using implicit differentiation.

c) Using the Derivative operation in Matheamtica, confirm your derivative from the previous step.

d) Find the derivatives (yes plural) when x = 1. Look at the function, how many points have an x-coordinate of 1?

e) Graph the tangent lines at these points on the same set of axes as the Lemniscate.

3) Now let’s look at another famous implicitly defined curve, the folium of Descartes. This curve is defined by: x^3 + y^3 = 6xy.

a) Plot the folium of Descartes.

b) In Mathematica write a detailed step by step process on how to find the derivative, dy/dx, by using implicit differentiation.

c) Using the Derivative operation in Matheamtica, confirm your derivative from the previous step.

d) Find all points where dy/dx = 0 (horizontal tangent lines). You should use Mathematica and the Solve or Reduce options.

e) Plot the horizontal tangent lines on the same plot as the folium.

f) We could also find the vertical tangent lines by looking where dy/dx is undefined. But, this function is its own inverse so if you reflex your horizontal tangent lines over the line y = x, you will find your vertical tangent lines. Try this to get the vertical tangent lines and plot them to confirm they are the vertical tangent lines.

 

Essay Help
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.