{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Final_exam_ _(13)

# Final_exam_ _(13) - MATH 241 FINAL EXAM Instructions Number...

This preview shows pages 1–2. 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: MATH 241 FINAL EXAM May 16, 2005 Instructions: Number the answer sheets from 1 to 9. Fill out all the information at the top of each sheet. Answer problem n on page n, n = 1, - - - ,9. Do not answer one question on more than one sheet. If you need more space use the back of the correct sheet. Please write out and sign the Honor Pledge on page 1 only. SHOW ALL WORK The Use of Calculators Is Not Permitted On This Exam 1. (25 points) Let A z (2, 1, ~1), B 2 (5,0,1). (a) Find parametric equations for the line L containing A and B. (b) Let F = yi + 2zj + 3xk. Find the work W done by the force F on an object moving from A to B along L. 2. (20 points) A particle moves along a curve C with speed given by Hv(t)H = 5V t2 + 9 for all 13. At time t : 4 the unit tangent vector to C is given by T(4) = %i + §j + gk. (a) Find v(4), the velocity of the particle at time t = 4. (b) If the acceleration at time t = 4 is a(4) 2 4i + 4k, ﬁnd the normal component of the acceleration at that time. 3. (15 points) Let f(:t, y) =2 6‘” cosy — sinus. Show that the plane tangent to the graph of f (at, y) at (0, 2 , 0) is parallel to, but not the same as, the plane a: + y + z 2 0. 4. (20 points) The Ace Widget Company has determined that 56 units of labor and y units of capital can produce f (:13, y) = 603:3/ 4311/ 4 heavy duty, left-handed Widgets. Also suppose that each unit of labor costs \$100 While each unit of capital costs \$200. Assume that \$40,000 is available to spend on production. How many units of labor and how many units of capital should be utilized in order to maximize production ? //s1n:r+y _ where R is the triangle with vertices (0 ,,0) (7r/2, 0) and (7r/2, 77/2). 5. (20 points) Compute 6. (20 points) Find the area A of the region bounded by the limacon 7" = 2 + cos 9. 7. (25 points) Use the transformation u 2 :c + y, 1) = :1: - y to ﬁnd f/R(:t — y)emz”y2 dA where R is the rectangular region bounded by the lines x+y=0,m+y=1,x~y=1,av—y=4. 8. (25 points) Let A = (0,0,0), B = (2, 0,0), D : (0,2,1). (a) Find the equation of the plane containing A, B and D. (b) Let F(;r, y, z) 2 —3y2i + 4zj + 696k Use Stokes’s theorem to calculate f0 F ' dr Where C’ is the triangle ABD oriented counter— clockwise as Viewed from above. 9. (30 points) (a) Compute 2 ————-——dV ///D x/x2+y2+22 where D is the set of (my, z) for which 1 g m2 + y2 + 22 S 9. (b) Let F(wyz)= xi+yj+zk 7 ’ x/rr2+y2+z2 Show that 2 V-F: V062 +1;2 +22 //EF-ndS where Z is the boundary of D and n is the outward unit normal. (c) Compute ...
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