{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ReviewTest2Spr08 - MAC 3473 Honors Calculus 2 Keesling...

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

View Full Document Right Arrow Icon
MAC 3473 Honors Calculus 2 Keesling Review Test #2 Test Date 3/3/08 1. Show that 1 n 3 n = 1 ! " converges. 2. Denote the limit by 1 n 3 n = 1 ! " = L . What must N be so that 1 n 3 ! L n = 1 N " < 1 10,000 ? 3. For what values of p does 1 n p n = 1 ! " converge? For what values of p does it diverge? 4. Show that 1 2 n n 3 n = 1 ! " converges using the Root Test. 5. For which values of x does x n 2 n n 3 n = 1 ! " converge? 6. For what values of x does x n n p n = 1 ! " converge for p > 1 ? For what values of x does it converge for 0 ! p ! 1 ? 7. Find a power series representation for arctan( x ) = a n x n n = 0 ! " . For which values of x does this power series converge? 8. Find a power series representation for f ( x ) = ln(1 + x ) = a n x n n = 0 ! " . For which values of x does this power series converge? 9. For which values of x do the following power series converge? (a) x n n n n = 1 ! " (b) x n n ! n = 0 ! " 10. (a) Determine the power series for sin x = a n x n n = 0 ! " . (b) What is the radius of convergence for the power series? (c) Show that the power series converges to sin x for all x for which it is defined.
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
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