M17 LE3 0909 - Mathematics 17 First Semester AY 2009-2010...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Mathematics 17 First Semester AY 2009-2010 Third Long Exam 5 September 2009 General Instructions. Use only blue or black ballpen. Show all necessary solutions and box all final answers. I. MODIFIED TRUE OR FALSE. Write TRUE if the statement is true. Otherwise, provide a brief justification why the statement is false. 2 pts each 1. For any positive real number a , a x > a y implies that x > y . 2. If a polynomial function f has real coefficients and odd degree, then f has to have at least one real root. 3. By Descartes’ Rule of Signs, the polynomial x 4 - x 2 + 2 x - 5 has exactly one negative real root. 4. If f ( x ) = x 2 - 1 x - 1 , then f - 1 exists and ( f - 1 f )( x ) = x for all real number x . 5. The sequence log 20 , log 40 , log 80 is an arithmetic progression with a common difference of 2. II. Do as indicated. 1. Given f ( x ) = 6 x 4 - x 3 + 5 x 2 - x - 1. (a) List all possible rational zeroes of f . 2 pts (b) Given that i is a zero of f , find all its other zeroes. (Do not use long division.) 4 pts 2. Determine the inverse and range of the function h ( x ) = x 3 + 1 x 3 - 1 . 5 pts 3. Find the exact value of (log
Image of page 1
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