DOC PREVIEW
MIT 18 01 - Exam -18.01

This preview shows page 1-2 out of 5 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

18.01 Exam 4 Name: Problem 1: /25 Problem 2: /25 Problem 3: /25 Problem 4: /25 Total: /100 Instructions: Please write your name at the top of every page of the exam. The exam is closed book, calculators are not allowed, but you are allowed to use your prepared index card. You will have approximately 50 minutes for this exam. The point value of each problem is written next to the problem – use your time wisely. Please show all work, unless instructed otherwise. Partial credit will be given only for work shown. You may use either pencil or ink. If you have a question, need extra paper, need to use the restroom, etc., raise your hand. 1� � � Name: Problem 1: /25 Problem 1(25 points) A solid is formed by revolving about the x-axis the region bounded by the x-axis, the line x = 0, the line x = a, and the curve, πx y = b sin . a Find the volume of the solid. You may use the half-angle formulas, cos2(θ/2) = (1 + cos(θ))/2, sin2(θ/2) = (1 − cos(θ))/2 2Name: Problem 2: /25 Problem 2(25 points) A solid is formed by revolving about the y-axis the region bounded by the x-axis, the line x = 0, the line x = a, and the curve, ab y = − b. x Find the volume of the solid. It is simplest to use the shell method. But you may use the disk method if you prefer. 3Name: Problem 3: /25 Problem 3(25 points) A surface is formed by revolving about the x-axis the curve, 3 y = x , 0 ≤ x ≤ 1. Since the curve is revolved about the x-axis, the radius of each slice is y. Compute the surface area of the surface. 4Name: Problem 4: /25 Problem 4(25 points) Sketch the polar curve, r(θ) = sin(θ) sin(θ + (π/2)), 0 ≤ θ ≤ π. Take note: the angle θ varies over only 1/2 of a complete revolution. In particular, label the following on your graph, (i) in which quadrant or quadrants the curve is contained, (ii) the endpoints of the curve, (iii) the two slopes of the tangent lines at the endpoints of the curve, (iv) and the angle or angles θ at which r(θ) is a maximum.


View Full Document

MIT 18 01 - Exam -18.01

Documents in this Course
Graphing

Graphing

46 pages

Exam 2

Exam 2

3 pages

Load more
Download Exam -18.01
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Exam -18.01 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Exam -18.01 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?