{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MAC 2312 Exam 2 - MAC 2312 Exam 2 Solutions July 7 2011...

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

View Full Document Right Arrow Icon
MAC 2312 Exam 2 Solutions July 7, 2011 Name: | {z } By writing my name, I swear by the honor code. Read all of the following information before starting the exam: Show all work, clearly and in order, if you want to get full credit. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct). Circle or otherwise indicate your final answers. This test has 5 problems and is worth 50 points, plus one bonus problem at the end. It is your responsibility to make sure that you have all of the pages! Since time is limited, it is crucial that you think before you compute. You must state any theorems or tests that you use. All hypotheses must be verified. Good luck!
Image of page 1

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

View Full Document Right Arrow Icon
1. Evaluate the integral. Z 2 x 2 - x + 1 x 3 + x dx Solution: The integrand is a proper rational function, so we use partial fractions. 2 x 2 - x + 1 x 3 + x = 2 x 2 - x + 1 x ( x 2 + 1) = A x + Bx + C x 2 + 1 Multiplying both sides by x ( x 2 + 1) yields 2 x 2 - x + 1 = A ( x 2 + 1) + ( Bx + C ) x. Plugging in x = 0 gives that A = 1. Then, expanding and equating coefficients gives B = 1 and C = - 1. Thus, Z 2 x 2 - x + 1 x 3 + x dx = Z dx x + Z x - 1 x 2 + 1 dx = ln | x | + Z x x 2 + 1 dx - Z dx x 2 + 1 .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern