review 4s11 - MAC 2311 Test Four Review Spring 2011 Exam...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MAC 2311 Test Four Review, Spring 2011 Exam covers Lectures 25 – 34, except lecture 29 Online Calculus Text, Chapter 4 sec. 24 and 26 – 30, plus Chapter 5, sec. 31 – 33 omit Chapter 4, sec. 25 and 29 1. On which interval(s) is f ( x ) = 1 2 x - 1 x 2 increasing and decreasing? Find all local extrema. 2. Find each interval on which the graph of f ( x ) = ( x 2 + 1) e x is both increasing and concave down. Find each inflection point. 3. Suppose that f ( x ) has horizontal tangent lines at x = - 2, x = 1 and x = 5. If f 00 ( x ) > 0 on intervals ( -∞ , 0) and (2 , ) and f 00 ( x ) < 0 on the interval (0 , 2), find the x -valuse at which f ( x ) has relative extrema. Find the x -value of each inflection point of f ( x ). Assume that f and each of its derivatives are continuous on ( -∞ , ). 4. Evaluate the following limits. Use L’Hospital’s Rule if it applies. a. lim x 0 x - ln( x + 1) 1 - sec 2 x b. lim x 0 cos 2 x e x/ 3 + 1 c. lim x 1 - ln(1 - x 2 ) ln(1 - x ) 2 d. lim x 1 (2 - x ) tan( πx/ 2) e. lim x →∞ ( e x + x ) 1 x f. lim x 0 (cot x - csc x ) 5. Find each horizontal asymptote of f ( x ) = x 2 e - x . Use L’Hospital’s Rule if necessary. Then sketch the graph of f ( x ), showing all local extrema and inflection points.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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