Math 2110Q Final Portfolio
数学final代做 Answer the questions directly in this document. You must complete ALL writing prompts and ALL math prompts. For the written part…
- Answer the questions directly in this document. You must complete ALL writing prompts and ALL math prompts. For the written part, you should type in complete sentences. For the parts asking for mathematical work, scan your work as a clear PDF or image and insert it in the document. A sample is provided.
- When you submit your work, it will be scanned using plagiarism detection software. This means that your typed explanations should be yours alone and show not look similar to other students or resources.
- Don’t use Chegg/Bartleby/other resources that answer direct questions. This is your (take home) final exam. You cannot post these questions online (except as outlined below). You cannot search for these exact questions or slight variations of these questions. You cannot view solutions to these questions on Chegg or other similar websites. If you use internet resources (e.g. general sites to help understand the material), you must provide references.
- You may ask questions during office hours (Gauss’s Garage), problem sessions or on Campuswire.
- When you are done, export the entire document as a PDF and upload to your discussion section HuskyCT page. It will be scanned with SafeAssign.
(3 points) Writing Prompt 1: Sometimes when evaluating a double integral, we need to change the order of integration or change from rectangular to polar coordinates. How do we know when we need to change coordinates? (typed 100-250 words)
(2 points) Math Prompt 1: Give an example of a situation where we need to change the order of integration and another where we need to change to polarcoordinates. (include a PDF or image)
(3 points) Writing Prompt 2: How do we think about changing the order of integration? Write out the steps you should take and how you should think about it. You may use the example you wrote above part of your explanation. (typed,100-200 words)
(2 points) Math Prompt 2: Show the steps of changing the order of integration of the example you gave in Math Prompt 1. Then evaluate the integral. (include a PDF or image)
(5 points) Math Prompt 3: The expression below can be represented by a single double integral if we use polar coordinates. Find that double integral. (include a PDF or image and one or two explanation sentences afterward)
Module 1: Three Dimensional Space (Chapter 12)
(3 points) Writing Prompt 1: (typed, 100-200 words) How can you determine if four points lie on the same plane? Explain your process in detail. 数学final代做
(6 points) Math Prompt 1:(include a PDF or image) Determine an equation of the plane which contains the points (1, 2, 3), (3, 4, 5), (-1, 2, 6), and (9, -7, 8) or explain why it is not possible.
Module 2: Differential Calculus in Two or More Variables (Chapter 14)
(3 points) Writing Prompt : (typed 100-200 words)
In your own words, define the level curves of a function of two variables. Describe how level curves can help you sketch a graph of a surface. Give examples of several surfaces whose level curves are circles and at least one example of a surface whose level curves are not circles.
(6 points) Math Prompt: (include a PDF or image)
Find the absolute maximum and absolute minimum of 𝑓(𝑥, 𝑦) = 𝑥3 − 𝑥𝑦 + 𝑦2 − 𝑥 on the closed triangular region with vertices (0,0), (2,0) and (0,2).
Module 3: Double and Triple Integrals (Chapter 15) 数学final代做
(3 points) Writing Prompt: (typed, 100-200 words)
When doing a triple integral, in what situations would you change to cylindrical or spherical coordinates? When do you want to evaluate in cartesian? Give an example of each of the three cases.
(6 points) Math Prompt: (include a PDF or image followed by a few sentences explaining your work)
Set up a triple integral to calculate the volume of a “the orange slice” between 𝑦 = cos(𝑥) 𝑧 = 𝑦 and 𝑧 = 0 using four (of the six) different orders of integration.
See https://www.geogebra.org/3d/qtqcww4jModule 4: Vector Functions (Chapter 13)
(3 points) Writing Prompt 1: (typed, 100-300 words) Consider the curve whose graph is given by 𝑦 = 𝑓(𝑥). In calculus 1, we learned how to find the tangent line to this curve. Then in this class, we learned how to parametrize the curve as 𝑟 →(𝑡) = 〈𝑡, 𝑓(𝑡)〉and then find the equation of the tangent line to that curve in parametric form. Explain, in words, how these two methods work. Do they give the same line?
Module 5: Parametric Curves and Line Integrals(Chapter 16, 16.1-16.4)
(6 points) Math Prompt 1:
(a) Find the parametrization of two different curves from the point (2,4) to (3,9).
(b) Compute the work done of the vector field 𝐹 over the two →= 〈2𝑥𝑦, 𝑥2 + 2〉curves found in part (a).
(c) Give an example of a curve from (2,4) to (3,9) that would give a different numerical value for the work done over the same vector field as in part (b) above, if possible. If it is not possible to find a curve that gives a different numerical value for the work done, explain why.
(3 points) Writing Prompt 2: (typed, 100-200 words) Let 𝐹 be a conservative vector →field and 𝐶 be a closed curve. Explain why the line integral over 𝐶 is 0 two ways: using both the Fundamental Theorem of Line Integrals and using Green’s Theorem.
Module 6: Parametric Surfaces and Surface Integrals (Chapter 16, 16.5-16.9)
(3 points) Writing Prompt 2: (typed, 50-150 words) We cannot use the Divergence Theorem on the surface integral in the previous part. Explain why we can’t use it and how we add and subtract something extra so that we can use Divergence Theorem but are still computing the same surface integral over the same region.
(3 points) Math Prompt 2: (include a PDF or image) Do the adaptation (the adding and subtracting) you mentioned above and find integral with divergence theorem.
Note: you should get the same value. 数学final代做