sampleExam-calculus-II.pdf - — Problem 1[2 x 8 Points...

This preview shows page 1 out of 1 page.

Problem 1 [2 x 8 Points]: Consider the function f ( x ) = x 2 in the interval [0 , 1]. a) Derive the Riemann sum of f ( x ) on the given interval for a regular partition. b) Using the result from a) compute R 1 0 f ( x ) dx . Problem 2 [3 x 9 Points]: Compute the following indefinite integrals using substitution or integration by parts: a) Z 2 x p 1 + x 2 dx , b) Z dx p x (1 + p x ) 2 , c) Z x cos(3 x ) dx . Problem 3 [3 x 9 Points]: Consider the function g ( x ) = ln( x ). a) Compute the Taylor polynomial of order 3 for g ( x ) at x 0 = 2. b) Write down the Lagrange remainder for the Taylor polynomial that you derived in a). c) Compute the Taylor series of g ( x ) at x 0 = 2. Problem 4 [8 Points]:
Image of page 1
You've reached the end of this preview.

{[ 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