Test 2B

# Test 2B - Test#2 Math 241 — Form B —— 100 points...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Test #2 Math 241 — Form B —— 100 points total *No calculators, No cell phones, No PDAs *No questions during the test unless there is a typing error *Please begin each problem at the top of a new page in the blue book *Write your name and row on the outside of the blue book. *Show all work. Mark out any work that you do not want graded. 1. Given the function f (x) = V9— x2 a) (6 pts) Setup only the deﬁnite integral to ﬁnd the average value of function on the interval [-3, 3]. b) (10 pts) Setup only the deﬁnite integrals to ﬁnd the centroid (ff) of the lamina of uniform density p bound by f(x) and the x—axis. 2. (6 pts) A function y(x) satisﬁes the following differential equation ; d . . . . E:- = xcos y 0 S y S 27: What are the equlllbrium solut1ons? 3. (10 pts) Given % = 2y — x with y(0) = 1, use Euler’s Method to 1 approximate y(l) using step size Ax = E 4. (28 pts) Solve the following differential equations a) (x2 +1)??? = xy y(0) = 1 (implicit solution) b) 2—? = 3w +1 w(0) = 2 (explicit solution) 5. For the following 3 problems, do not integrate BUT be sure to completely set the deﬁnite integrals. Draw a picture that clearly shows your set—up; label your variables, label the direction of your x or y axis, label where x= or y= 0 is on your ﬁgure , etc. a) (10 pts) A force of 10 lbs is required to stretch a spring from its natural length of 1 ft. to 1.5 ft. How much work is done in stretching the spring from its natural length to a length of 3ft. ? b) (10 pts) A gate in an irrigation canal is in the form of a trapezoid 4 ft wide at the bottom, 8 ft. wide at the top, with height equal to 2 feet. It is placed vertically in the canal with the water extending 10 feet above the top of the gate. The density of water is 62.4lb/ ﬁts. Find the hydrostatic force on the gate. c) (10 pts) A tank full of oil (density is SOlb / ft3 ) has the shape of a paraboloid of revolution (that is, the shape is obtained by rotating a parabola about a vertical axis). If the height is 6 ft and the radius at the top is 6 ft, ﬁnd the work required to pump the oil over the rim of the tank. 6. (10 pts) Find the orthogonal trajectories of the family of curves x = kyz. Name the conic section for each family. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern