makeup_240_f2011

# makeup_240_f2011 - Makeup Final Exam Math 240 Calculus III...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Makeup Final Exam, Math 240: Calculus III September, 2011 No books, papers or may be used, other than a hand-written note sheet at most 8 . 5 00 × 11 00 in size. All electronic devices must be switched off during the exam. This examination consists of nine (9) long answer questions and one (1) true/false question. Partial credits will be given only when a substantial part of a long answer question has been worked out. Merely displaying some formulas is not sufficient ground for receiving partial credits. • Your name, printed: • Your Penn ID (last 4 of the middle 8 digits): My signature below certifies that I have complied with the University of Pennsylvania’s code of academic integrity in completing this examination. Your signature 1 2 3 4 5 6 7 8 9 10 Total Name: 1 1. For what values of k is the following matrix singular? 2- 3 1 2 k- k- 6 4 Ans. k = . Name: 2 2. Consider the following differential equation x (1- x ) d 2 dx 2 + (3- 4 x ) d dx- 2 u ( x ) = 0 . (a) Find a real number μ such that there exists a solution of the form u ( x ) = x μ · 1 + X n ≥ 1 a n x n !...
View Full Document

## This note was uploaded on 03/06/2012 for the course MATH 240 taught by Professor Storm during the Fall '08 term at UPenn.

### Page1 / 12

makeup_240_f2011 - Makeup Final Exam Math 240 Calculus III...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online